I guess the main problem is how to give a reasonable output regarding the naive assumptions cos(x)=sqrt(1-sin(x)^2) asin(sin(x))=x without having specified a domain of definition for x? Of course, we expect to get the usual answers, however, a correct output should either complain about missing dom or then give a principal- or preferably all branches. In this sense the current output is just as only a part of the truth as the expected one?
On Friday, 26 September 2014 02:37:27 UTC+2, Bill Page wrote: > > It seems to me that algebraically any transformation that eliminates or > adds an extra sqrt is likely incorrect. So I would say that (1) in your > example is very suspicious. > > On 25 September 2014 20:04, kfp <[email protected] <javascript:>> wrote: > >> >> Indeed. Since we get >> >> (1) -> normalize sqrt(1-sin(z)^2) >> >> z 2 >> tan(-) - 1 >> 2 >> (1) ----------- >> z 2 >> tan(-) + 1 >> 2 >> *but* >> >> Type: Expression(Integer) >> (2) -> normalize cos(z) >> >> z 2 >> - tan(-) + 1 >> 2 >> (2) ------------- >> z 2 >> tan(-) + 1 >> 2 >> >> it's accountable. BTW OpenAxiom gives a correct answer. >> >> >> >>> But also >>> >>> (1) -> complexNormalize acos(cos(z)) >>> >>> (1) - z >>> >>> >>> >>> -- >> You received this message because you are subscribed to the Google Groups >> "FriCAS - computer algebra system" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected] <javascript:>. >> To post to this group, send email to [email protected] >> <javascript:>. >> Visit this group at http://groups.google.com/group/fricas-devel. >> For more options, visit https://groups.google.com/d/optout. >> > > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
