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/*  English character strings used in MathXpert
    Do not translate text within dollar signs.
    Translate text included in quotation marks using ISO-Latin1 character set
    Sent to translator 8.12.97
    8.19.98:   1968 is changed.
    8.20.98    more strings added
    9.22.98    1859, 1912, 334 corrected.
    9.29.98    2161 corrected.
    11.8.98    2314 added, number of 2312 corrected to 2313
    1.6.99     2316 etc. added
    1.7.99     more added
    1.22.99    modified; french2 is in sync at this point.
    2.19.99    last modified
    Sent to German translator
    3.19.99    added 2361,...
    3.23.99    added 2365,
    3.30.99    modified 1878
    7.18.99    added missing $  $ at 1996 ff.
    10.14.99   added 2391
    1.2.00     added 2392
    1.9.00     added spaces in 2357
    1.9.00     added 2393
    1.10.00    added 2394-95
    1.15.00    added 2396
    2.2.00     added 2397,2398,2399,2400
    2.3.00     added 2401, 2402
    2.26.00    added 2403
    2.28.00    added 2404
        That was the last change in version 1.42 (revision 0)
    3.24.00    added 2405 to 2420
    4.2.00     added 2421 and 2422
    4.21.00 added 2423,2424,2425
    5.06.00 added 2426
    6.24.00 added 2427
    7.12.00 added 2428-2447
    7.17-19.00 added up to 2461
    7.23.00    added 2463 and 2463
    7.24.00   changed 1968, 2273, 2255-59
    3.13.01  added 2464 and 2465
    6.16.04  added 2466 and 2467
    6.18.04  added 2468
    6.21.04  added 2469 and 2470
    6.23.04 added 2471 and 2472
    6.24.04 added 2473-78 and 2255
    8.7.04  added 2479
    8.26.04 added 2480
    8.28.04 added 2481
    9.3.04 removed a superfluous include
    9.5.04  changed MathXpert to MathXpert globally
    9.11.04 added strings through 2491
    9.12.04 altered 2070
    9.12.04 added 2492-94
    10.10.04 added 2495-2497
    10.31.04 changed 2068, added 2498-2501
	1.23.06 added 2506
*/

#include <assert.h>
#define ENGLISH_DLL
#include "export.h"   /* Do not translate this or the next 3 lines */
#include "english1.h"
/*____________________________________________________________________________*/

static const char * english_strings2[] =
{
"write as square",                                                  /* 1850 */
"write as cube",                                                    /* 1851 */
"express in form a^?",                                              /* 1852 */
"Assuming the new square roots are defined. ",                      /* 1853 */
"The resulting expression is equal to the previous one only subject ", /* 1854 */
"to those assumptions.  For example, its graph may be different.",  /* 1855 */
"You can only convert a specific, numerical angle to degrees.",     /* 1856 */
"Definition of a new variable cannot be constant.",                 /* 1857 */
"The group entered must be a sum.",                                 /* 1858 */
"$a\\sqrt b = \\sqrt (a^2b)$ if $a\\ge 0$",                                          /* 1859 */
"The factor outside the square root must be nonnegative",           /* 1860 */
"The factor outside the root must be nonnegative",                  /* 1861 */
"$a(^n\\sqrt b)=^n\\sqrt (a^nb)$(n odd)",                                          /* 1862 */
"$a(^n\\sqrt b)=^n\\sqrt (a^nb)$ ($a\\ge 0$)",                                         /* 1863 */
"Would you like to regard the variables occurring non-linearly ",   /* 1864 */
"as constants and proceed to solve for the other variables?",       /* 1865 */
"Inappropriate problem",                                            /* 1866 */
"Too many windows",                                                 /* 1867 */
"You have solved the equations, but perhaps the answers should be simplified.", /* 1868 */
"You have solved the equation, but MathXpert would take one more step.", /* 1869 */
"You have solved the equation, but perhaps the answer should be simplified.", /* 1870 */
"Because the topic is Trig Addition, a solution using a trig addition ", /* 1871 */
"formula will be given, instead of a shorter solution using periodicity.",      /* 1872 */
"Although a formula for the singularities has been calculated, it was too hard for MathXpert to find their numerical values.",  /* 1873 */
"MathXpert calculation",                                             /* 1874 */
"MathXpert graph",                                                   /* 1875 */
"Please enter a positive integer. Zero is not positive.",           /* 1876 */
"$-^n\\sqrt a = ^n\\sqrt (-a)$ if n odd",                                         /* 1877 */
"The original cubic must have more than one real root.  In that case complex solutions of the equations you have derived will give rise to real solutions of the original equation, but complex numbers are not used in this topic.", /* 1878 */
"There can be at most three roots of a cubic equation.  Simplify the expressions for the roots until some of them are identical.",  /* 1879 */
"rationalize denom    and simplify",   /* space to make 'and' start in the 22nd character */ /* 1880 */
"Enter the new exponent: ",                                         /* 1881 */
"You have solved the equation, but the answer should still be simplified.", /* 1882 */
"The selected topic requires MathXpert PreCalculus Assistant.",      /* 1883 */
"The selected topic requires MathXpert Calculus Assistant.",         /* 1884 */
"Illegal topic for Algebra",                                        /* 1885 */
"Illegal topic for Precalculus",                                    /* 1886 */
"The file %s is read-only. You cannot write into that file.",       /* 1887 */
"The file %s already exists. Do you wish to replace it?",           /* 1888 */
"The file %s is a hidden or system file.  You cannot open it.",     /* 1889 */
"The file %s cannot be opened.  Probably the file is damaged.",     /* 1890 */
"Too many files already open.  Close files open in other applications.", /* 1891 */
"Directory %s does not exist.",                                     /* 1892 */
"%s is not a legal filename.",                                      /* 1893 */
"File %s does not exist.",                                          /* 1894 */
"The function values could be calculated only at isolated points, so no graph is visible.  The reason could be that some intermediate numbers were too large or too small, or it could be that the function is really only defined at isolated points.", /* 1895 */
"File is not a valid MathXpert document.",                           /* 1896 */
"Complex numbers are not in use.",                                  /* 1897 */
"This law is not valid for real roots.",                            /* 1898 */
"Too many solutions will result.",                                  /* 1899 */
"substitute specific   integers",                                   /* 1900 */
/* 'integers' begins at character 22; the space is important. */
"a=-b becomes $a^2=-b^2$  if $a,b \\ge  0$",                              /* 1901 */
"a=-b becomes a=0     if $a,b \\ge  0$",                                /* 1902 */
"a=-b becomes b=0     if $a,b \\ge  0$",                                /* 1903 */
"A function with that same name has already been defined.  You can redefine it or undefine it, but not define it.", /* 1904 */
" from file ",                                                      /* 1905 */
"$lim(t\\to ""\\pm \\infty ,cos t)$      is undefined",                            /* 1906 */
"$lim(t\\to ""\\pm \\infty ,sin t)$      is undefined",                            /* 1907 */
"$lim(t\\to ""\\pm \\infty ,tan t)$      is undefined",                            /* 1908 */
"Limit of the denominator is not defined and not plus or minus infinity.", /* 1909 */
"Limit of the numerator is not defined and not plus or minus infinity.", /* 1910 */
"$a/^n\\sqrt b = ^n\\sqrt (a^n/b)$     (n odd or $a\\ge 0$)",                          /* 1911 */
"$^n\\sqrt a/b = ^n\\sqrt (a/b^n)$     (n odd or $b>0$)",                          /* 1912 */
"$\\sqrt a/b = \\sqrt (a/b^2)$ if $b>0$",                                        /* 1913 */
"$a/\\sqrt b = \\sqrt (a^2/b)$ if $a\\ge 0$",                                        /* 1914 */
"Numerator must be non-negative",                                   /* 1915 */
"Denominator must be non-negative",                                 /* 1916 */
"Enter the first new exponent:",                                    /* 1917 */
"First evaluate the derivative.",                                   /* 1918 */
"File ",                                                            /* 1919 */
"No equation is solved for a derivative of a variable.",            /* 1920 */
"eliminate derivative",                                             /* 1921 */
"You have already differentiated the equation.",                    /* 1922 */
"You must solve each equation, either for a derivative or a variable.", /* 1923 */
"Limit of denominator is undefined.",                               /* 1924 */
"Is ", /* first part of 'Is x the independent variable?' */         /* 1925 */
"This law is not generally valid; what is under the root must be real.", /* 1926 */
"What is under the root must be negative.",                         /* 1927 */
"sg(x) = 1 if x > 0",                                               /* 1928 */
"sg(x) = -1 if x < 0",                                              /* 1929 */
"sg(x)=|x|/x          (x nonzero)",                                 /* 1930 */
"sg(x)=x/|x|          (x nonzero)",                                 /* 1931 */
"d/dx sg(u) = 0       (u nonzero)",                                 /* 1932 */
"$\\int sg(u)v dx=sg(u)\\int v dx$ (u nonzero)",                              /* 1933 */
"Expression inside sg may be zero.",                                /* 1934 */
"The expression inside the sg function cannot be positive.",        /* 1935 */
"sg(x)=1 assuming x>0",                                             /* 1936 */
"The expression inside the sg function cannot be negative.",        /* 1937 */
"sg(x)=-1 assuming x<0",                                            /* 1938 */
"Enter  n = integer - k, where n is the variable to change.",       /* 1939 */
"sg(ax) = sg(x) if a>0",                                            /* 1940 */
"sg(ax) = -sg(x) if a<0",                                           /* 1941 */
"sg(ax/b)=sg(x), a/b>0",                                            /* 1942 */
"sg(ax/b)=-sg(x),a/b<0",                                            /* 1943 */
"MathXpert cannot calculate that limit.",                            /* 1944 */
"The resulting numerator and denominator would both be undefined.", /* 1945 */
"The resulting numerator and denominator would both be zero.",      /* 1946 */
"The resulting denominator would be zero, and MathXpert can't determine its sign.", /* 1947 */
"Multiply one factor and divide the other by what?",                               /* 1948 */
"One limit would be zero and the other undefined.",                 /* 1949 */
"Format of mathpert.toc is illegal. If you altered it, restore the original.  If not, reinstall MathXpert.", /* 1950 */
"That expression is real, but it is negative, so it's not in polar form, which is $re^(it)$ with $r$ positive.", /* 1951 */
"That expression still contains a product of trig functions.",      /* 1952 */
"Initial value of function",                                        /* 1953 */
"Initial value of derivative",                                      /* 1954 */
"Initial value of second derivative",                               /* 1955 */
"Initial value of third derivative",                                /* 1956 */
"Initial value of fourth derivative",                               /* 1957 */
"First evaluate the limit.",                                        /* 1958 */
"$lim a/u^2 = \\infty $ if $lim u = 0$    and $a > 0$",             /* 1959 */
"$lim a/u^2 = -\\infty $ if $lim u = 0$    and $a < 0$",                        /* 1960 */
"$lim a/u^2^n = \\infty $ if $lim u = 0$    and $a > 0$",                        /* 1961 */
"$lim a/u^2^n =-\\infty $ if $lim u = 0$    and $a < 0$",                        /* 1962 */
"$lim u^n = (lim u)^n$ requires $lim u$ to be defined, infinite, or oscillatory, ",   /* 1963 */
"MathXpert cannot verify either condition.",                         /* 1964 */
"That is not the case here.",                                       /* 1965 */
"Eliminate zero denominators.",                                     /* 1966 */
"or when $u$ is nonnegative or nonpositive.",                       /* 1967 */
"Evaluate to apply the divergence test",                            /* 1968 */
"$lim uv = lim u lim v$ can fail if $lim u = 0$ and $lim v$ is undefined.", /* 1969 */
"Enter one term of the new sum: ",                                  /* 1970 */
"This inequality is too complicated for MathXpert to graph.",        /* 1971 */
"$a < \\sqrt u$ iff $0 \\le  u$     provided a < 0",                          /* 1972 */
"$a \\le  \\sqrt u$ iff $0 \\le  u$     provided $a \\le  0$",                        /* 1973 */
"$\\sqrt u > a$ iff $u \\ge  0$     provided a < 0",                          /* 1974 */
"$\\sqrt u \\ge  a$ iff $u \\ge  0$     provided $a \\le  0$",                        /* 1975 */
"$a < ^2^n\\sqrt u$ iff $0 \\le  u$   provided a < 0",                          /* 1976 */
"$a \\le  ^2^n\\sqrt u$ iff $0 \\le  u$   provided $a \\le  0$",                        /* 1977 */
"$^2^n\\sqrt u > a$ iff $u \\ge  0$   provided a < 0",                          /* 1978 */
"$^2^n\\sqrt u \\ge  a$ iff $u \\ge  0$   provided $a \\le  0$",                        /* 1979 */
"One of the factors is zero.",                                      /* 1980 */
"One of the factors is, or simplifies to, zero.",                   /* 1981 */
"If not, you may get a wrong answer, so be careful.",               /* 1982 */
"MathXpert will assume it is defined and nonzero.",                  /* 1983 */
"MathXpert is assuming that what is under the square root is nonnegative.", /* 1984 */
"It is possible to make contradictory assumptions and arrive at wrong answers.", /* 1985 */
"Therefore, keep an eye on your assumptions.",                      /* 1986 */
"Base of exponent must be positive.",                               /* 1987 */
"There is an unevaluated infinite or undefined subterm.",           /* 1988 */
"Denominator too complicated to expand in partial fractions.",      /* 1989 */
"you must first prepare for it by using ",                          /* 1990 */
"Before you are ready to use ",                                     /* 1991 */
"You might try ",                                                   /* 1992 */
"!This equation can be solved for the original integral.",          /* 1993 */
"!provided this limit turns out to be zero.",                       /* 1994 */
"Input not acceptable",                                             /* 1995 */
"$(e^(-t)-1)/t\\to $",                                                  /* 1996 */
"$(sinh t)/t\\to $",                                                    /* 1997 */
"$(tanh t)/t\\to $",                                                    /* 1998 */
"$(cosh t-1)/t\\to $",                                                  /* 1999 */
"$(1-cosh t)/t\\to $",                                                  /* 2000 */
"$(cosh x-1)/x^2\\to \\onehalf $ as $x\\to $",                                        /* 2001 */
"Disabled",                                                         /* 2002 */
"Restricted Trial",                                                 /* 2003 */
"The problem file for this topic has been altered.  Restore the original problem files or re-install MathXpert.", /* 2004 */
" from ",                                                          /* 2005 */
"Previous",                                                        /* 2006 */
"Next",                                                            /* 2007 */
"Help",                                                            /* 2008 */
"Edit",                                                            /* 2009 */
"Paste",                                                           /* 2010 */
"Problem Number",                                                  /* 2011 */
"Source",                                                          /* 2012 */
"Equations valid for all times:",                                  /* 2013 */
"Equations valid for only one time:",                              /* 2014 */
"Graph Number",                                                    /* 2015 */
"Domain and Range", /* dialog title and button text, so keep it short */  /* 2016 */
"Style",                                                           /* 2017 */
"Riemann Sums",                                                    /* 2018 */
"From",                                                            /* 2019 */
"to",                                                              /* 2020 */
"Number of Intervals",                                             /* 2021 */
"Style of Sum",                                                    /* 2022 */
"Simpson's Rule",                                                  /* 2023 */
"Trapezoid Rule",                                                  /* 2024 */
"Is this what you meant?",                                         /* 2025 */
"Point and Slope",                                                 /* 2026 */
"Original",                                                        /* 2027 */
"Current",   /* as in Current Line, as opposed to Original Line */ /* 2028 */
"Slope",                                                           /* 2029 */
"Selected Point",                                                  /* 2030 */
"Active",     /* as in, Active Parameter */                        /* 2031 */
"is now",                                                          /* 2032 */
"with increment",                                                  /* 2033 */
"After parameter changes",                                         /* 2034 */
"Erase old graphs",                                                /* 2035 */
"Show all graphs",                                                 /* 2036 */
"Parameters",                                                      /* 2037 */
"Initial Values",                                                  /* 2038 */
"After changing initial values",                                   /* 2039 */
"Graph Colors",                                                    /* 2040 */
"Color",                                                           /* 2041 */
"Border",                                                          /* 2042 */
"Function",                                                        /* 2043 */
"Background",                                                      /* 2044 */
"Axes",                                                            /* 2045 */
"with",                                                            /* 2046 */
"Title is",                                                        /* 2047 */
"Ranges",                                                          /* 2048 */
"Horizontal",                                                      /* 2049 */
"Vertical",                                                        /* 2050 */
"First Graph",                                                     /* 2051 */
"Second",                                                          /* 2052 */
"Third",                                                           /* 2053 */
"Fourth",                                                          /* 2054 */
"Fifth",                                                           /* 2055 */
"Sixth",                                                           /* 2056 */
"Restore Original",                                                /* 2057 */
"Parametric Graph Ranges",                                         /* 2058 */
"Parameter",                                                       /* 2059 */
"Ensure circles are round",                                        /* 2060 */
"Polar Graph Ranges",                                              /* 2061 */
"Angle",                                                           /* 2062 */
"Textbook Selection",                                              /* 2063 */
"Select a textbook",                                               /* 2064 */
"About MathXpert",                                                  /* 2065 */
"Design and implementation:  Michael Beeson",                      /* 2066 */
"",                                                                /* 2067 */
"Book dialog: Dave Empey",                                         /* 2068 */
"Translation: ",  /* translator, insert your name */               /* 2069 */
"Splash screen art: Cindi Shih",                                   /* 2070 */
"",                                                                /* 2071 */
"Copyright � 2004 Help With Math ",                                /* 2072 */
"",                                                                /* 2073 */
"Please wait",                                                     /* 2074 */
"Print",                                                           /* 2075 */
"Left Header",                                                     /* 2076 */
"Right Header",                                                    /* 2077 */
"Size and Position of Graph",                                      /* 2078 */
"Inches",                                                          /* 2079 */
"Centimeters",                                                     /* 2080 */
"Left Margin",                                                     /* 2081 */
"Top Margin",                                                      /* 2082 */
"Close this calculation?",                                         /* 2083 */
"Don't ask this question in the future",                           /* 2084 */
"If you turn off confirmation here, you can turn it back on from the Options menu.", /* 2085 */
"Open problem file",                                               /* 2086 */
"Close problem file",                                              /* 2087 */
"Open .mxp file",                                                  /* 2088 */
"Exit",               /* as in, exit the program */                /* 2089 */
"Save",                                                            /* 2090 */
"Save as",                                                         /* 2091 */
"Print now",                                                       /* 2092 */
"Assumptions",                                                     /* 2093 */
"Author's Commentary",                                             /* 2094 */
"Functions",                                                       /* 2095 */
"Define a function",                                               /* 2096 */
"Redefine a function",                                             /* 2097 */
"Undefine a function",                                             /* 2098 */
"Show functions",                                                  /* 2099 */
"Always request confirmation",                                     /* 2100 */
"Never request confirmation",                                      /* 2101 */
"Formulas",                                                        /* 2102 */
"Highlighted Formulas",                                            /* 2103 */
"Selected Formulas",                                               /* 2104 */
"Justifications",                                                  /* 2105 */
"Restore Factory Colors",                                          /* 2106 */
"Type Size",                                                       /* 2107 */
"Bigger",                                                          /* 2108 */
"Smaller",                                                         /* 2109 */
"Normal",                                                          /* 2110 */
"Tool Bar",                                                        /* 2111 */
"Large Icons",                                                     /* 2112 */
"Small Icons",                                                     /* 2113 */
"Decimals",                                                        /* 2114 */
"Large Numbers",                                                   /* 2115 */
"Sound",                                                           /* 2116 */
"On",                                                              /* 2117 */
"Off",                                                             /* 2118 */
"Confirm Close",                                                   /* 2119 */
"Language",                                                        /* 2120 */
"Operations",                                                      /* 2121 */
"Show Operations Menu",                                            /* 2122 */
"Hide Operations Menu",                                            /* 2123 */
"Cascade",                                                         /* 2124 */
"Tile",                                                            /* 2125 */
"Arrange Icons",                                                   /* 2126 */
"Close All",                                                       /* 2127 */
"Contents",                                                        /* 2128 */
"Search for Help on...",                                           /* 2129 */
"Using help",                                                      /* 2130 */
"Ticks",    /* as in, ticks on a graph--small marks by the axes */ /* 2131 */
"Normal",                                                          /* 2132 */
"None",                                                            /* 2133 */
"Multiples of Pi",                                                 /* 2134 */
"Axes Labels",                                                     /* 2135 */
"Numbers",                                                         /* 2136 */
"Letters",                                                         /* 2137 */
"No Labels",                                                       /* 2138 */
"Change Colors",                                                   /* 2139 */
"All Graphs",                                                      /* 2140 */
"Singularities",                                                   /* 2141 */
"Jumps",                                                           /* 2142 */
"Hide Titles",                                                     /* 2143 */
"Show Grid",                                                       /* 2144 */
"Approximate Integration",                                         /* 2145 */
"Differential Equations",                                          /* 2146 */
"$^n\\sqrt (-a) = -^n\\sqrt a, n odd$",                                          /* 2147 */
"$a<u^2<b$ => $-\\sqrt b<u<-\\sqrt a$  or $\\sqrt a<u<\\sqrt b$",                           /* 2148 */
"$a\\le u^2\\le b$ => $-\\sqrt b\\le u\\le -\\sqrt a$  or $\\sqrt a\\le u\\le \\sqrt b$",                           /* 2149 */
"$a<u^2\\le b$ => $-\\sqrt b\\le u<-\\sqrt a$  or $\\sqrt a<u\\le \\sqrt b$",                           /* 2150 */
"$a\\le u^2<b$ => $-\\sqrt b<u\\le -\\sqrt a$  or $\\sqrt a\\le u<\\sqrt b$",                           /* 2151 */
"$a < u^2^n$ iff          $u<-^2^n\\sqrt a$ or $^2^n\\sqrt a<u$",                    /* 2152 */
"$a\\le u^2$ iff $u\\le -\\sqrt a$ or $\\sqrt a\\le u$",                                    /* 2153 */
"$a<u^2^n<b$ => $-^2^n\\sqrt b<u<-^2^n\\sqrt a$ or $^2^n\\sqrt a<u<^2^n\\sqrt b$",                   /* 2154 */
"$a\\le u^2^n\\le b$ => $-^2^n\\sqrt b\\le u\\le -^2^n\\sqrt a$ or $^2^n\\sqrt a\\le u\\le ^2^n\\sqrt b$",                   /* 2155 */
"$a<u^2^n\\le b$ => $-^2^n\\sqrt b\\le u<-^2^n\\sqrt a$ or $^2^n\\sqrt a<u\\le ^2^n\\sqrt b$",                   /* 2156 */
"$a\\le u^2^n<b$ iff $-^2^n\\sqrt b<u\\le -^2^n\\sqrt a$ or $^2^n\\sqrt a\\le u<^2^n\\sqrt b$",                  /* 2157 */
"$\\sqrt (a^2^n)=a^n$ if $a^n\\ge 0$",                                           /* 2158 */
"$|sin u| \\le  u$ if $u\\ge 0$",                                          /* 2159 */
"$|arctan u| \\le  u$ if $u\\ge 0$",                                       /* 2160 */
"$|tan u| \\le  u$ if $0\\le u\\le \\pi /2$",                                      /* 2161 */
"$lim(x\\to a,c) = c$       (c constant)",  /* spaces important */     /* 2162 */
"$lim c^v=c^(lim v)$,     (c constant > 0)", /* spaces important*/ /* 2163 */
"compute factorial",                                               /* 2164 */
"shift sum limits",                                                /* 2165 */
"$\\sum  cu = c\\sum  u$ (c const)",                                         /* 2166 */
"proved by induction",                                             /* 2167 */
"defn of $d^nu/dx^n$",                                               /* 2168 */
"differentiate matrix",                                            /* 2169 */
"     for power series",      /* spaces important */               /* 2170 */
"$\\sqrt a/b = \\sqrt (a/b^2)$ if b>0",                                         /* 2171 */
"$\\sqrt a/b= -\\sqrt (a/b^2)$ if b<0",                                         /* 2172 */
"(b>0 or n odd)",                                                  /* 2173 */
"(b<0, n even)",                                                   /* 2174 */
"if $a\\ge 0$",                                                        /* 2175 */
"if $a\\le 0$",                                                        /* 2176 */
"(n odd or $a\\ge 0$)",                                                /* 2177 */
"(n even and $a\\le 0$)",                                              /* 2178 */
"if $-\\pi /2\\le \\theta \\le \\pi /2$",                                                 /* 2179 */
"if $0\\le \\theta \\le \\pi $",                                                      /* 2180 */
"is       undefined",   /* translator, make 'undefined' begin in the same column */  /* 2181 */
"$\\sqrt (-a) = i\\sqrt a$ if $a\\ge 0$",                                          /* 2182 */
"Number inside ln must be in polar form.",                         /* 2183 */
"Number inside $\\sqrt $ must be in polar form.",                        /* 2184 */
"Number inside $^n\\sqrt $ must be in polar form.",                       /* 2185 */
"Use \"clear denom of i\" instead",                                /* 2186 */
"[p=a,p=-a] and $p\\ge 0$   iff p=|a|",  /* translator, make iff come out in the same column */ /* 2187 */
"|u| = u iff $0 \\le  u$",                                               /* 2188 */
"|u| = -u iff $u \\le  0$",                                              /* 2189 */
"$0\\le u/v$ => 0<uv or u=0",                                            /* 2190 */
"$u/v\\le 0$ => uv<0 or u=0",                                            /* 2191 */
"(if n is odd)",                                                     /* 2192 */
"$u^2<a iff -\\sqrt a < u < \\sqrt a$",                                           /* 2193 */
"$a<u^2 iff u<-\\sqrt a or \\sqrt a<u$",                                          /* 2194 */
"$a\\le u^2 iff u\\le -\\sqrt a or \\sqrt a\\le u$",                                          /* 2195 */
"$-a<x^2<b$ iff $x^2<b$",                                              /* 2196 */
"$-a\\le x^2\\le b$ iff $x^2\\le b$",                                              /* 2197 */
"$-a<x^2\\le b$ iff $x^2\\le b$",                                              /* 2198 */
"$-a\\le x^2<b$ iff $x^2<b$",                                              /* 2199 */
"$u^2^n < a$ iff          $-^2^n\\sqrt a < u < ^2^n\\sqrt a$",                         /* 2200 */
"$u^2^n \\le  a$ iff          $-^2^n\\sqrt a \\le  u \\le  ^2^n\\sqrt a$",                         /* 2201 */
"$u^2\\le a iff -\\sqrt a \\le  u \\le  \\sqrt a$",                                           /* 2202 */
"cancel",                                                            /* 2203 */
"cancel gcd",                                                        /* 2204 */
"polynomial division",                                               /* 2205 */
"Divide row ",              /* space at end is important */          /* 2206 */
"by",                                                                /* 2207 */
"Add",                                                               /* 2208 */
"times",    /* as in 'four times eight' */                           /* 2209 */
"row",                                                               /* 2210 */
"to row",   /* as in, 'add row 3 to row 4' */                        /* 2211 */
"Sub",      /* as in, 'Subtract', but keep it short */               /* 2212 */
"from row",                                                          /* 2213 */
"matrix multiplication",                                             /* 2214 */
"formula for 2 by 2              ", /* keep the same length */       /* 2215 */
"matrix inverse",                                                    /* 2216 */
"compute inverse",                                                   /* 2217 */
"convert matrix eqn",             /* 21 characters max */            /* 2218 */
          /* means, convert matrix equation to list of ordinary equations */
"where   cos ",   /* preserve length by using more or less space after 'where' */   /* 2219 */
"in",                                                                /* 2220 */
"$a|b| = |ab|$ if $0 \\le  a$",                                          /* 2221 */
"a|b|/c = |ab/c|      if $0\\le a/c$",                                   /* 2222 */
"Completing the square requires a non-constant linear term.",        /* 2223 */
"This equation is solved, but it is customary to put the variable on the left side, so MathXpert would take one more step.", /* 2224 */
"OK",                                                                /* 2225 */
"!Assuming the previous right side is nonnegative. ",                /* 2226 */
"Find the extrema on ",                                              /* 2227 */
"You must compute a table of function values and select the maximum or minimum.", /* 2228 */
"You should select the maximum and/or the minimum to complete the problem.", /* 2229 */
"!No minimum or maximum on this interval",                           /* 2230 */
"Find the extrema.",                                                 /* 2231 */
"This operation cannot be applied to an improper integral ",         /* 2232 */
"unless the integrand is nonnegative.",                              /* 2233 */
"There is an unevaluated infinite series.",                          /* 2234 */
"MathXpert cannot find a closed form for this series.",               /* 2235 */
"The general term does have a finite limit.",                        /* 2236 */
"telescoping series",                                                /* 2237 */
"MathXpert cannot compute the limit of the general term.",            /* 2238 */
"Expression to shift by cannot depend on the index variable.",       /* 2239 */
"(n odd)",                                                           /* 2240 */
"function is constant",                                              /* 2241 */
"Max and min are the same for a constant function.",                 /* 2242 */
"It is not necessary, and will not help, to take the derivative.",   /* 2243 */
"Perhaps you are trying to reject an endpoint.",                     /* 2244 */
"You can't insert more than 1000 new terms.",                        /* 2245 */
"add to index variable",                                             /* 2246 */
"subtract from        index variable",                               /* 2247 */
"How many terms do you want explicitly written out?",                /* 2248 */
"Decrease the lower limit of summation by how much?",                /* 2249 */
"Add what to the index variable?",                                   /* 2250 */
"Subtract what from the index variable?",                            /* 2251 */
"Decrease lower limit",                                              /* 2252 */
"MathXpert cannot check the convergence of the series that would result.", /* 2253 */
"The resulting series would be divergent, so the law cannot be applied.", /* 2254 */
"The function being defined cannot be used in the definition.",      /* 2255 */
"Evaluate to apply the integral test",                               /* 2256 */
"Evaluate to apply the root test",                                   /* 2257 */
"Evaluate to apply the ratio test",                                  /* 2258 */
"Evaluate to apply the comparison test",                             /* 2259 */
"The general term is not decreasing.",                               /* 2260 */
"MathXpert cannot determine that the general term is decreasing.",    /* 2261 */
"!The series is convergent.  ",                                      /* 2262 */
"!The series is divergent.  ",                                       /* 2263 */
"Some assumptions have been made.",                                  /* 2264 */
"!The test was inconclusive.",                                       /* 2265 */
"finish integral test",                                              /* 2266 */
"finish root test",                                                  /* 2267 */
"finish ratio test",                                                 /* 2268 */
"finish comparison test",                                            /* 2269 */
"finish divergence test",                                            /* 2270 */
"You must first evaluate the limit, or undo.",                       /* 2271 */
"The comparison term does not contain the summation variable.",      /* 2272 */
"Evaluate to apply the limit comparison test",                       /* 2273 */
"finish limit         comparison test",                              /* 2274 */
"The test worked; the problem is reduced to the convergence of this series.  ", /* 2275 */
"Cannot verify the required inequality",                             /* 2276 */
"Enter the general term of the comparison series",                   /* 2277 */
"The new integrals would not be defined, so this operation is illegal.", /* 2278 */
"The integrand is not defined on the entire interval of integration.",   /* 2279 */
"You should break it into two or more integrals first.",             /* 2280 */
"The integrand is undefined somewhere besides the left endpoint." ,  /* 2281 */
"The integrand is undefined somewhere besides the right endpoint." , /* 2282 */
"MathXpert cannot evaluate the limit.",                               /* 2283 */
"The limit is zero.",                                                /* 2284 */
"limit of integrand    is not zero",  /* at most 21 chars before the spaces */ /* 2285 */
"Although there are singularities, the integrand is nonnegative, ",  /* 2286 */
"so the integral is infinite rather than just undefined.",           /* 2287 */
"There are singularities.  You might be able to get the answer ",    /* 2288 */
"$\\infty $ or $-\\infty $ if you first break the integral, unless it contains ",  /* 2289 */
"infinities of both signs.",                                         /* 2290 */
"When both limits are infinite, you must break the integral first. ", /* 2291 */
"The limits at the two ends must exist separately.",                 /* 2292 */
"limit of integrand    is undefined",                                /* 2293 */
"condensation test",                                                 /* 2294 */
"finish condensation  test",                                         /* 2295 */
"!The test worked. The series is convergent. Assumptions may have been made. ", /* 2296 */
"!The test worked. The series is convergent.",                       /* 2297 */
"!The test worked.  The series is divergent.",                       /* 2298 */
"The limit of the general term is not zero.",                        /* 2299 */
"You started the divergence test, but didn't finish it yet.",        /* 2300 */
"You started the integral test, but didn't finish it yet.",          /* 2301 */
"You started the comparison test, but didn't finish it yet.",        /* 2302 */
"You started the limit comparison test, but didn't finish it yet.",  /* 2303 */
"You started the condensation test, but didn't finish it yet.",      /* 2304 */
"You started the root test, but didn't finish it yet.",              /* 2305 */
"You started the ratio test, but didn't finish it yet.",             /* 2306 */
"The convergence or divergence is not yet settled.",                 /* 2307 */
"calculate first terms",                                             /* 2308 */
"Maximum number of first terms to add is about 128,000.",            /* 2309 */
"Lower index of sum cannot exceed sixteen million.",                 /* 2310 */
"Calculate the sum of the first how many terms?",                    /* 2311 */
"!If this series converges, so does the original series.",           /* 2312 */
"!If this series diverges, so does the original series.",            /* 2313 */
"The answer must be expressed in terms of the original variable or variables.", /* 2314 */
" is not correct.   Cannot switch to that language.",  /* Translator, leave the initial space */              /* 2315 */
"express series as     $a_0 + a_1 + ...$",                           /* 2316 */
"express series as     $a_0 + a_1 + a_2 + ...$",                     /* 2317 */
"express series using  ... and general term",                        /* 2318 */
"show more terms      before ...",                                   /* 2319 */
"express series using sigma notation",                               /* 2320 */
"show another term    before ...",                                   /* 2321 */
"The maximum number of terms before ... is 1000.",                   /* 2322 */
"How many more terms do you want to see?",                           /* 2323 */
"solve for constant   of integration",                               /* 2324 */
"The resulting series would not converge.",                          /* 2325 */
"The resulting series would converge only at isolated points",       /* 2326 */
"integrate power      series term by term",                          /* 2327 */
"differentiate        term by term",                                 /* 2328 */
"MathXpert cannot open the file %s.  It may be in another folder, or the name may have been misspelled.  If you clicked on a Web page to open a MathXpert document, the hyperlink is not valid.",  /* 2329 */
"You must first rename one of the summation variables.",             /* 2330 */
"multiply series",                                                   /* 2331 */
"multiply power series",                                             /* 2332 */
"divide power series",                                               /* 2333 */
"add series",                                                        /* 2334 */
"subtract series",                                                   /* 2335 */
"Lower limits of summation are not the same.",                       /* 2336 */
"Upper limits of summation are not the same.",                       /* 2337 */
"You must rename one or more of the summation variables first.",     /* 2338 */
"binomial series",                                                   /* 2339 */
"First rewrite one or both of the series, to arrange that the exponents have the same coefficient of the summation variable.", /* 2340 */
"First term in the denominator must be the constant term.",          /* 2341 */
"MathXpert requires numerical coefficients for series division.",     /* 2342 */
"Constant term must be nonzero for series division.",                /* 2343 */
"There are too many function definitions.  Undefine a function to make room for the definition of the coefficients of the quotient.", /* 2344 */
"MathXpert cannot verify that the recursion will terminate.",         /* 2345 */
"Function argument must be an integer.",                             /* 2346 */
"Function argument too large.",                                      /* 2347 */
"compute function     value",                                        /* 2348 */
"show terms with      factorials evaluated",                         /* 2349 */
"show coefficients in decimal form",                                 /* 2350 */
"do not use decimal   form for coefficients",                        /* 2351 */
"do not evaluate      factorials",                                   /* 2352 */
"MathXpert requires numerical coefficients for series exponentiation.", /* 2353 */
"Exponent must be a number.",                                        /* 2354 */
"express $(\\sum  a_k x^k)^n$   as a series",                             /* 2355 */
"Leading coefficient must be nonzero for series exponentiation.",    /* 2356 */
"  if  ",  /* 2 leading and 2 trailing spaces are important here */  /* 2357 */
"otherwise",                                                         /* 2358 */
"express as power of ?",                                             /* 2359 */
"Enter the desired base: ",                                          /* 2360 */
"Cannot draw the graph",                                             /* 2361 */
"Function is not a non-constant polynomial for the current parameter value.  Change the parameter value.", /* 2362 */
"Function is not a non-constant polynomial for the current parameter values.  Change the parameter values.", /* 2363 */
"It is not correct to apply this operation to an improper integral.",/* 2364 */
"Select problem file",                                               /* 2365 */
"Find the minimum and maximum of",                                   /* 2366 */
"on the interval",                                                   /* 2367 */
"Cannot open problem file",                                          /* 2368 */
"The specified problem file could not be found or is incorrectly formatted.", /* 2369 */
"Sorry, the term you entered is not a factor.",                      /* 2370 */
"The law $ln ab = ln a + ln b$ is not always correct. ",             /* 2371 */
"The two sides can differ by a multiple of $2\\pi i$ .",                 /* 2372 */
"For example, try the case when $a$ and $b$ are both $-1$.",         /* 2373 */
"!Assuming that the radius is positive.",                            /* 2374 */
/* The following lines specify text for the buttons.
   It is important that these remain SHORT in translation. */
"Range",                              /* on Graph Toolbar*/          /* 2375 */
"Redraw",                                                            /* 2376 */
"Next",                                                              /* 2377 */
"Prev",                                                              /* 2378 */
"Edit",                                                              /* 2379 */
"&Undo",            /* Calculation toolbar buttons, or Speedbar */    /* 2380 */
"&Hint",                                                              /* 2381 */
"Auto&Step",                                                          /* 2382 */
"Sho&wStep",                                                          /* 2383 */
"&AutoFinish",                                                        /* 2384 */
"&Finished",                                                          /* 2385 */
"&Graph",                                                             /* 2386 */
"&Prev",        /* repeated on purpose for Speedbar */                /* 2387 */
"&Edit",                                                              /* 2388 */
"&Next",                                                              /* 2389 */
"UHSWAFGPEN",   /* Hot keys as specified by ampersands above, all uppercase */ /* 2390 */
"graphs",                                                             /* 2391 */
"Integration by parts cannot be applied to improper integrals directly.  First express the integral as a limit.", /* 2392 */
"That function is still in use.  To redefine it you must first close all calculations and graphs that mention it.", /* 2393 */
"Can't verify exponent is even.",                           /* 2394 */
"Exponent is not even.",                                    /* 2395 */
"Solution(s) should be reduced to the form $a + bi$.",              /* 2396 */
"Division by zero is not allowed.",                         /* 2397 */
"That would produce the useless equation 1 = 1, since any nonzero number to the zero-th power is 1.", /* 2398 */
"That would produce the useless equation 0 = 0, since zero raised to any nonzero power is zero.",     /* 2399 */
"That would produce a fraction with zero in the denominator, which is not defined.", /* 2400 */
"That expression is already in the form $u+iv$.",              /* 2401 */
"Expression should be reduced to the form $a + bi$.",          /* 2402 */
"result of            comparison test",                        /* 2403 */
"You still need to state the final result of the comparison test for the original series.", /* 2404 */
"Red",                                                         /* 2405 */
"Gray",                                                        /* 2406 */
"Blue",                                                        /* 2407 */
"Green",                                                       /* 2408 */
"Cyan",                                                        /* 2409 */
"Magenta",                                                     /* 2410 */
"Yellow",                                                      /* 2411 */
"White",                                                       /* 2412 */
"Black",                                                       /* 2413 */
"thin",                                                        /* 2414 */
"thick",                                                       /* 2415 */
"no ticks",                                                    /* 2416 */
"normal ticks",                                                /* 2417 */
"ticks at n pi",                                               /* 2418 */
"Please use a color different from the background.",           /* 2419 */
"and",                                                         /* 2420 */
"$-a \\le u \\le a$ iff $|u|\\le a$",                          /* 2421 */
"$-a < u < a$ iff $|u|<a$",                                    /* 2422 */
"MathXpert Algebra Assistant",                                  /* 2423 */
"MathXpert Precalculus Assistant",                              /* 2424 */
"MathXpert Calculus Assistant",                                 /* 2425 */
" by ",  /* as in Divide eqn 4 by 3 */                         /* 2426 */
"Select Graph Paper",                                          /* 2427 */
"Adjust to Graph Paper",                                       /* 2428 */
"Automatically adjust colors",                                 /* 2429 */
"Title",                                                       /* 2430 */
"Title Background",                                            /* 2431 */
"Light blue",                                                  /* 2432 */
"Medium blue",                                                 /* 2433 */
"Light orange",                                                /* 2434 */
"Light green",                                                 /* 2435 */
"Medium gray",                                                 /* 2436 */
"Light gray",                                                  /* 2437 */
"Light yellow",                                                /* 2438 */
"Light violet",                                                /* 2439 */
"Apply changes to",                                            /* 2440 */
"Graph 1",                                                     /* 2441 */
"Graph 2",                                                     /* 2442 */
"Graph 3",                                                     /* 2443 */
"Graph 4",                                                     /* 2444 */
"Graph 5",                                                     /* 2445 */
"Graph 6",                                                     /* 2446 */
"Please use a title color different from the background.",     /* 2447 */
"Please use an axes color different from the background.",     /* 2448 */
"Please use a border color different from the background.",    /* 2449 */
"Please use a function color different from the background.",  /* 2450 */
"Please use function colors different from the background.",   /* 2451 */
"Width",                                                       /* 2452 */
"Height",                                                      /* 2453 */
"Landscape",                                                   /* 2454 */
"Portrait",                                                    /* 2455 */
"Whole page, with specified margins",                          /* 2456 */
"Maximum size",                                                /* 2457 */
"Same shape as on screen",                                     /* 2458 */
"Center vertically",                                           /* 2459 */
"Center horizontally",                                         /* 2460 */
"Save settings without printing",                              /* 2461 */
"Left margin plus graph width cannot exceed paper width.",     /* 2462 */
"Top margin plus graph height cannot exceed paper height.",    /* 2463 */
"Graph width must be positive.",                               /* 2464 */
"Graph height must be positive.",                              /* 2465 */
"tan(t/2) is undefined somewhere in the interval of integration.", /* 2466 */
"MathXpert cannot verify that tan(t/2) is defined on the interval of integration.", /* 2467 */
"Negative real numbers have no complex square roots.",         /* 2468 */
"$(a^(i\\theta))^(1/n) = a^(b/n)$ only when $$-pi < theta <= pi$$",           /* 2469 */
"First write a in polar form.",                                /* 2470 */
"Cannot redefine a built-in function.",                        /* 2471 */
"Equality sign expected.",                                     /* 2472 */
"$\\sqrt(bi)= \\sqrt(b/2)+\\sqrt(b/2)i$  if b >= 0",           /* 2473 */
"$\\sqrt(-bi)= \\sqrt(b/2)-\\sqrt(b/2)i$  if b >= 0",          /* 2474 */
"$\\sqrt(a+bi)= \\sqrt((a+c)/2)+\\sqrt((a-c)/2)i$  if b >= 0 and c=\\sqrt(a^2+b^2)", /* 2475 */
"$\\sqrt(a-bi)= \\sqrt((a+c)/2)-\\sqrt((a-c)/2)i$ if b >= 0 and c=\\sqrt(a^2+b^2)",  /* 2476 */
"There is a repeated variable on the left side.",              /* 2477 */
"You have already used that letter on the right side of another definition.", /* 2478 */
"ac=bc iff a=b or c=0",                                        /* 2479 */
"Cannot redefine a function that is in use.  Close all calculations or graphs that use this function, then redefine it.", /* 2480 */
"The selected expression must contain the variable of integration.",  /*  2481 */
"The file you tried to open contains a user-defined function that is already defined.  First close any open documents and choose Function | Undefine function from the menu, then try again to open this file.",  /* 2482 */
"Your free evaluation period has # days remaining after today.",   /* 2483 */
"Activate",                                                        /* 2484 */
"Continue Evaluation",                                             /* 2485 */
"Purchase Now",                                                    /* 2486 */
"You can convert your evaluation version to the purchased version by entering a valid serial number and pressing Activate.", /* 2487 */
"You can purchase a valid serial number at www.HelpWithMath.com.",  /* 2488 */
"Evaluation Version",                                               /* 2489 */
"Your evaluation version of MathXpert has expired.",                /* 2490 */
"Exit MathXpert",                                                   /* 2491 */
"Make a Graph",                                                     /* 2492 */
"Work a Problem",                                                   /* 2493 */
"Run a Demo",                                                       /* 2494 */
"Point, Slope, and Parameter",                                      /* 2495 */
"Radians",                                                          /* 2496 */
"Degrees",                                                          /* 2497 */
"Go to Help With Math's web site",                                  /* 2498 */
"Send email to Help With Math",                                     /* 2499 */
"Author's essay about MathXpert",                                   /* 2500 */
"Switch MathXpert to the specified language",                       /* 2501 */
"Double vertical range",                                            /* 2502 */
"Halve vertical range",                                             /* 2503 */
"Double horizontal range",                                          /* 2504 */
"Halve horizontal range",                                           /* 2505 */
"Enter the new lower limit of summation:",                          /* 2506 */
""
};

/*____________________________________________________________________________*/
const char *english2(int n)
{ return english_strings2[n];
}

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