Re: [fricas-devel] [BUG] bug in "pairsum" causes wrong integration result
oldk1331 wrote: > On 7/14/19 9:26 PM, Waldek Hebisch wrote: > > Real bug above is that we can not expand terms separately. > > Concerning "pairsum": it should go away. I with attached > > patch I get: > > > > (1) -> integrate(a^(1/4)/(x^8-1),x) > > > >(1) > >4+-+ > >--+x\|a - 8 %E > >> %E log() > >--+4+-+ > > 4 \|a > > 4096 %E - a = 0 > >+ > >4+-+ > >--+x\|a - 8 %F > >> %F log() > >--+4+-+ > > 4 \|a > > 4096 %F + a = 0 > > Type: > Union(Expression(Integer),...) > > > > Unfortunatly, this causes troubles for definite integrator. > > Basically, we need to teach 'limit' how to handle 'rootSum'. > > > > Shouldn't we try to simplify 'rootSum' with coefficients like > "%E^4 +- a = 0"? We should try to simplify when we can. My point is: - 'rootSum' gives valid result when we can not simplify - compared to 'rootSum' some transformations that we currently do produce more complicated result, so we should drop them - once we have 'zeroOf' correct simplification is harder than with 'rootSum' - several simplifications depends on factorization. That requires global point of view, that is we need to look at all kernels. Currently implementation does not look at interactions between kernels and that is core of the problem. -- Waldek Hebisch -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/E1hoRKa-0005C3-JQ%40hera.math.uni.wroc.pl. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] [BUG] bug in "pairsum" causes wrong integration result
On 7/14/19 9:26 PM, Waldek Hebisch wrote: > Real bug above is that we can not expand terms separately. > Concerning "pairsum": it should go away. I with attached > patch I get: > > (1) -> integrate(a^(1/4)/(x^8-1),x) > >(1) >4+-+ >--+x\|a - 8 %E >> %E log() >--+4+-+ > 4 \|a > 4096 %E - a = 0 >+ >4+-+ >--+x\|a - 8 %F >> %F log() >--+4+-+ > 4 \|a > 4096 %F + a = 0 > Type: Union(Expression(Integer),...) > > Unfortunatly, this causes troubles for definite integrator. > Basically, we need to teach 'limit' how to handle 'rootSum'. > Shouldn't we try to simplify 'rootSum' with coefficients like "%E^4 +- a = 0"? -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/CAGBJN90BM0-ucsS-NAhPNSZEzNRHycfTK5MLyqsmbiiknrO97Q%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
Re: [fricas-devel] [BUG] bug in "pairsum" causes wrong integration result
oldk1331 wrote: > > Some faulty integration: > > integrate(a^(1/4)/(x^8-1),x) > -- following examples are from mapleok.input > in1867a:=integrate(1/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z) > in1869a:=integrate(1/(z^2-1)*(1-1/(I*z)^(1/2))^(1/2), z) > in1870a:=integrate(1/(z^2-1)/(1+(I*z)^(1/2))^(1/2), z) > > They are returning 0, which is obviously incorrect. > > Also > in1724a:=integrate(-z^2/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z) > is wrong, although its return value is not 0. > > > The problem happens in "pairsum" in irexpand.spad. > > This "pairsum" function tries to avoid cases like both > x^(1/n) and (-x)^(1/n) (where n is even) appears in result. > > Take "integrate(a^(1/4)/(x^8-1),x)" for example, in order to > solve "?^4+a/4096" appeared in > "split internalIntegrate(a^(1/4)/(x^8-1),x)", > "lg2func" uses "zeroOf" to introduce (-a)^(1/4) which causes > "pairsum" to return empty result. > > I suggest: > > 1. Add a warning/error in "pairsum" when it tries to return empty. > 2. We can handle cases like "?^4+a" "?^4+a*?^2+b" in "lg2func" better. First, 'zeroOf' should be used only when we know that polynomial is irreducible. Unfortunatly, current "lg2func" has too little information to do this correctly. AFIACS instead of current "lg2func" and friends we should use a variant of 'normalize'. And we need to extend 'normalize' so that it looks at algebraic dependencies. Anything less is just a temporary stopgap. Real bug above is that we can not expand terms separately. Concerning "pairsum": it should go away. I with attached patch I get: (1) -> integrate(a^(1/4)/(x^8-1),x) (1) 4+-+ --+x\|a - 8 %E > %E log() --+4+-+ 4 \|a 4096 %E - a = 0 + 4+-+ --+x\|a - 8 %F > %F log() --+4+-+ 4 \|a 4096 %F + a = 0 Type: Union(Expression(Integer),...) Unfortunatly, this causes troubles for definite integrator. Basically, we need to teach 'limit' how to handle 'rootSum'. -- Waldek Hebisch -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/E1hmeWE-0003fj-LL%40hera.math.uni.wroc.pl. For more options, visit https://groups.google.com/d/optout. --- ../ax-build128/src/algebra/IR2F.spad2019-06-16 14:23:33.853365732 + +++ IR2F.spad 2019-07-14 14:20:49.497966525 + @@ -151,16 +151,12 @@ zero?(d := degree(p := lg.coeff)) => error "poly has degree 0" (d = 1) => [linear(p, lg.logand)] d = 2 => quadratic(p, lg.logand, x) - odd? d and -((r := retractIfCan(reductum p)@Union(F, "failed")) case F) => -pairsum([cmplex(alpha := rootSimp zeroOf p, lg.logand)], -lg2func([lg.scalar, - (p exquo (monomial(1, 1)$UP - alpha::UP))::UP, - lg.logand], x)) [lg2cfunc lg] lg2cfunc lg == - +/[cmplex(alpha, lg.logand) for alpha in zerosOf(lg.coeff)] +s := new()$Symbol +ss := s::F +rootSum(ss*log((lg.logand)(ss)), lg.coeff, s) mkRealFunc(l, x) == ans := empty()$List(F)
[fricas-devel] [BUG] bug in "pairsum" causes wrong integration result
Some faulty integration: integrate(a^(1/4)/(x^8-1),x) -- following examples are from mapleok.input in1867a:=integrate(1/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z) in1869a:=integrate(1/(z^2-1)*(1-1/(I*z)^(1/2))^(1/2), z) in1870a:=integrate(1/(z^2-1)/(1+(I*z)^(1/2))^(1/2), z) They are returning 0, which is obviously incorrect. Also in1724a:=integrate(-z^2/(z^2-1)*(1-(I*z)^(1/2))^(1/2), z) is wrong, although its return value is not 0. The problem happens in "pairsum" in irexpand.spad. This "pairsum" function tries to avoid cases like both x^(1/n) and (-x)^(1/n) (where n is even) appears in result. Take "integrate(a^(1/4)/(x^8-1),x)" for example, in order to solve "?^4+a/4096" appeared in "split internalIntegrate(a^(1/4)/(x^8-1),x)", "lg2func" uses "zeroOf" to introduce (-a)^(1/4) which causes "pairsum" to return empty result. I suggest: 1. Add a warning/error in "pairsum" when it tries to return empty. 2. We can handle cases like "?^4+a" "?^4+a*?^2+b" in "lg2func" better. -- 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 fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/CAGBJN93UMzAehRuyyMFbp8afRXf%3DBsbKpKF2Jbnkrd7kb9r86Q%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
