OpenMath CD Basic

OpenMath Function Names

:: Asir/OpenXM (OpenXM 対応の asir) は OpenMath の Content Dictionaries に対応した, 以下の函数名をサポートする.

Basic_Pi = @pi $
Basic_true = 1$
Basic_false = 0$
Basic_e = @e$
def basic_plus(A,B) { return(A+B); }
def basic_times(A,B) { return(A*B); }
def basic_minus(A,B) { return(A-B); }
def basic_over(A,B) { return(A/B); }
def basic_power(A,B) { return(A^B); }
def basic_and(A,B)   { return(A && B); }
def basic_or(A,B)    { return(A || B); }
def basic_not(A)   { return(! A); }
def basic_IntegerQuotient(A,B) { return(idiv(A,B)); }
def basic_IntegerRemainder(A,B) { return(irem(A,B)); }
def basic_IntegerGcd(A,B)  { return(igcd(A,B)); }
def basic_exp(A)           { return(exp(A)); }
def basic_ln(A)            { return(log(A)); }
def basic_sin(A)           { return(sin(A)); }
def basic_cos(A)           { return(cos(A)); }
def basic_tan(A)           { return(tan(A)); }
def basic_diff(A,B)        { return(diff(A,B)); }
def basic_equal(A,B)       { return( A == B); }
def basic_unequal(A,B)     { return( A != B); }
def basic_less(A,B)        { return( A < B); }
def basic_lessequal(A,B)        { return( A <= B); }
def basic_greater(A,B)        { return( A > B); }
def basic_greaterequal(A,B)        { return( A >= B); }
def basic_select(A,B)         { return(A[B]); }
def basic_length(A)           { if (type(A)==4) return(length(A)); 
                                else return(size(A)[0]); }
Poly_lexicogrpahic = 2$
Poly_gradedLexicographic = 1$
Poly_gradedReverseLexicographic = 0$
def poly_degreeWrt(A,B)       { return(deg(A,B)); }
def poly_factor(A) { return(fctr(A)); }
def poly_gcd(A,B)  { return(gcd(A,B)); }
def poly_resultant(A,B,V) { return(res(V,A,B)); }
def poly_groebner(O,P,V)  { return(gr(P,V,O)); }
def poly_hilbert_polynomial(I,V,S)  { return(subst(hilbert_polynomial(I,V),h,S)); }

basic_ などがつかないつぎのような函数名も登録してある.

def factor(F) { return(poly_factor(F)); }
def cancel(F)  { return(red(F)); }
def numerator(F) { return(nm(F)); }
def denominator(F) { return(dn(F)); }
def hilbert_polynomial(G,V) {
     A=gr(G,V,0); B=map(dp_ht,map(dp_ptod,A,V));
     C=map(dp_dtop,B,V);
     return(sm1_hilbert([C,V]));
}

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