Please subscribe to the email list: 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.
On 23 October 2015 at 11:59, Thomas Baruchel <[email protected]> wrote: > I think the package is ready now; > > https://github.com/baruchel/numerical-routines/tree/master/spad > > The PSLQ (which was once selected as one of the "Top Ten Algorithms of the > Century) (see: https://en.wikipedia.org/wiki/Integer_relation_algorithm ) is > an algorithm useful for detecting integer relations between numerical > values. Thus it is a very useful algorithm for "experimental mathematics". > > See some example below: > * computing a numerical value with three other constants and then find > back the coefficients; > * finding the coefficients for the relation [gamma(11/2),1,sqrt(Pi)] > * detecting the algebreaic equation for which the golden number is a > solution (ie. detecting that phi actually is an algebraic number) > > The session below shows these three examples: > > (1) -> )lib PSLQ > Pslq is now explicitly exposed in frame initial > Pslq will be automatically loaded when needed from > /home/pi/docs/maths/numerical-routines/spad/PSLQ.NRLIB/PSLQ > (1) -> digits(64) > > (1) 20 > Type: > PositiveInteger > (2) -> z := numeric( 4 + 3/2*%pi - %e) > > (2) > 5.9941071519_2564462233_3677603566_5918285385_0700536269_9156495449_261 > Type: > Float > (3) -> v := oneDimensionalArray([z, 1.0, %pi, %e]) > > (3) > [5.9941071519_2564462233_3677603566_5918285385_0700536269_9156495449_261, > 1.0, > 3.1415926535_8979323846_2643383279_5028841971_6939937510_5820974944_592, > 2.7182818284_5904523536_0287471352_6624977572_4709369995_9574966967_628] > Type: > OneDimensionalArray(Expression(Float)) > (4) -> pslq(v, 1.0E-36) > > (4) [- 2.0,8.0,3.0,- 2.0] > Type: > OneDimensionalArray(Float) > (5) -> g := Gamma(11/2)$DoubleFloatSpecialFunctions > > (5) 52.342777784553526 > Type: > DoubleFloat > (6) -> w := oneDimensionalArray([g :: Float, 1.0, sqrt(%pi)]) > > (6) > [52.3427777845_5352603259_5982542261_4812850952_1484375, 1.0, > 1.7724538509_0551602729_8167483341_1451827975_4945612238_7128213807_79] > Type: > OneDimensionalArray(Expression(Float)) > (7) -> pslq(w, 1.0E-10) > > (7) [- 32.0,0.0,945.0] > Type: > OneDimensionalArray(Float) > (8) -> phi := numeric( (1+sqrt(5))/2 ) > > (8) > 1.6180339887_4989484820_4586834365_6381177203_0917980576_2862135448_623 > Type: > Float > (9) -> x := oneDimensionalArray([1,phi,phi^2]) > > (9) > [1.0, > 1.6180339887_4989484820_4586834365_6381177203_0917980576_2862135448_623, > 2.6180339887_4989484820_4586834365_6381177203_0917980576_2862135448_623] > Type: > OneDimensionalArray(Float) > (10) -> pslq(x, 1.0E-24) > > (10) [1.0,1.0,- 1.0] > Type: > OneDimensionalArray(Float) > (11) -> > > > -- > 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. -- 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.
