Hi there,
in the following session, numer_denom is computed several times on the same expression (using the up-arrow history recall mechanism):
$ ./ginsh ginsh - GiNaC Interactive Shell (GiNaC V1.1.1) __, _______ Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, (__) * | Germany. This is free software with ABSOLUTELY NO WARRANTY. ._) i N a C | You are welcome to redistribute it under certain conditions. <-------------' For details type `warranty;'.
Type ?? for a list of help topics.
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {-1264*d,-1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {-1264*d,-1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {1264*d,1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {-1264*d,-1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {-1264*d,-1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {1264*d,1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {-1264*d,-1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {1264*d,1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {1264*d,1264}
numer_denom((-(4/79*I)*(-1/8+(1/8*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))*sqrt(79))*d-(3/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)+(3/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(-3/32-(3/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(3/32-(3/32*I)*sqrt(79))*sqrt(79)+(-(4/79*I)*(-1/32-(1/32*I)*sqrt(79))*sqrt(79)-(4/79*I)*(1/32-(1/32*I)*sqrt(79))*sqrt(79)+(4/79*I)*(1/8-(1/8*I)*sqrt(79))^2*sqrt(79)-(4/79*I)*(1/8+(1/8*I)*sqrt(79))^2*sqrt(79))*c-3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))^3+3/4*(-(1/8-(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(1/8-(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8-(1/8*I)*sqrt(79))-3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))+3/4*((1/8+(1/8*I)*sqrt(79))^2-(1/4*I)*sqrt(79)+(-1/8+(1/8*I)*sqrt(79))*(1/8+(1/8*I)*sqrt(79)))^(-1)*(1/8+(1/8*I)*sqrt(79))^3); {-1264*d,-1264}
There are two problems here: (1) the numerator and denominator returned are trivially not coprime; and (2) numer_denom does not behave like a mathematical function. With the same input, it produces the sequence of answers
{-1264*d,-1264} {-1264*d,-1264} {1264*d,1264} {-1264*d,-1264} {-1264*d,-1264} {1264*d,1264} {-1264*d,-1264} {1264*d,1264} {1264*d,1264} {-1264*d,-1264}
All the best
Roberto
participants (1)
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Roberto Bagnara