# ----------------------------------------------------------------------------- # Distributed Maple application software # EXAMPLES file # # (c) 1998-2000, RISC-Linz, see file COPYRIGHT # http://www.risc.uni-linz.ac.at/software/distmaple # $Id: EXAMPLES,v 1.5 2001/07/26 05:35:30 schreine Exp $ # ----------------------------------------------------------------------------- # ----------------------------------------------------------------------------- # session startup # ----------------------------------------------------------------------------- # this is a complete distributed maple session read `dist.maple`; # use the machines of your choice dist[initialize]([ [thetys,`linux-fast`], [clio,`linux-fast`], [athena,`linux-fast`], [milkyway,`octane`], [milkyway,`octane`], [pinwheel,`octane`], [pinwheel,`octane`] ]); # start visualization dist[visualize](600,300,2,120); # load the application package read `distsoft/init.maple`; # ----------------------------------------------------------------------------- # parallel discriminant of a bivariate polynomial # ----------------------------------------------------------------------------- p := randpoly([x,y],expons=rand(0..30),coeffs=rand(0..1000),terms=50): `dist/maple/discrim`(p, x): # ----------------------------------------------------------------------------- # parallel gcd of univariate polynomials # ----------------------------------------------------------------------------- infolevel[gcd] := 9; p := randpoly([x],expons=rand(0..5*10^3),coeffs=rand(0..10^199),terms=10): q := randpoly([x],expons=rand(0..5*10^3),coeffs=rand(0..10^199),terms=10): r := randpoly([x],expons=rand(0..5*10^3),coeffs=rand(0..10^199),terms=10): `dist/gcd`(expand(p*q),expand(p*r)): infolevel[gcd] := 0; # ----------------------------------------------------------------------------- # parallel real root isolation # ----------------------------------------------------------------------------- # sequential 300s # p:=randpoly([x],expons=rand(0..300),terms=50,coeffs=rand(0..1000)); p := 437*x^181+954*x^122+642*x^5+724*x^37+646*x^34+265*x^280+434*x^113+173*x^72+615* x^167+498*x^195+1168*x^258+365*x^147+433*x^3+300*x^13+269*x^94+710*x^128+650* x^95+217*x^60+944*x^11+547*x^255+465*x^177+728*x^299+985*x^208+679*x^279+861*x ^28+613*x^29+697*x^23+420*x^66+632*x^73+241*x^75+280*x^39+308*x^52+89*x^134+ 760*x^85+890*x^90+942*x^98+173*x^152+694*x^171+77*x^207+15*x^213+61*x^223+644* x^228+274*x^268+52*x^276+607*x^242+720*x^286+738*x^270: `dist/maple/realroot`(p); # ----------------------------------------------------------------------------- # parallel resultant computation # ----------------------------------------------------------------------------- # something like this occurs in the plotting of an algebraic plane curve p:=randpoly([y],expons=rand(0..30),terms=50,coeffs=rand(0..10^10)): q:=randpoly([x,y],expons=rand(0..30),terms=50,coeffs=rand(0..10^10)): `dist/maple/resultant`(p,q,y): # ----------------------------------------------------------------------------- # parallel computation of singularities of a plane algebraic curve # ----------------------------------------------------------------------------- # p := randpoly([x,y], expons = rand(0..20),terms=20); # degree 37 # 280 s on Octane p:= 54*y^14*x^15+62*y^2*x^12-10*y^17*x^4-41*x^17*y^20-49*y^8*x^10-19*x^13*y+57*x^ 20-75*x^19+38*y^6*x^12-37*y^20*x^5-2*x^2*y^6-21*x^7-72*x^12*y^4-65*y^7*x+12*y^ 6*x^11-75*x^19*y-62*y^18*x^6-75*x^12*y+79*y*x^14+32*y^11*x^16: `dist/maple/singularities`(p, x, y); # ----------------------------------------------------------------------------- # parallel factorization of a univariate polynomial over a finite field # ----------------------------------------------------------------------------- p := 437*x^181+954*x^122+642*x^5+724*x^37+646*x^34+265*x^280+434*x^113+173*x^72+615* x^167+498*x^195+1168*x^258+365*x^147+433*x^3+300*x^13+269*x^94+710*x^128+650* x^95+217*x^60+944*x^11+547*x^255+465*x^177+728*x^299+985*x^208+679*x^279+861*x ^28+613*x^29+697*x^23+420*x^66+632*x^73+241*x^75+280*x^39+308*x^52+89*x^134+ 760*x^85+890*x^90+942*x^98+173*x^152+694*x^171+77*x^207+15*x^213+61*x^223+644* x^228+274*x^268+52*x^276+607*x^242+720*x^286+738*x^270: m := 2^31-1: `dist/maple/Berlekamp`(p, m); # ----------------------------------------------------------------------------- # # the remaining functions depend on CASA # # ----------------------------------------------------------------------------- # ----------------------------------------------------------------------------- # parallel plotting of a plane algebraic curve # ----------------------------------------------------------------------------- # sequential 800s plotsetup(x11); p:=-55*x^4*y^3+40*y-78*y^7+88*x^5*y^8+81*x^8*y+4*x^4*y^8+57*x^5*y^7-11*x*y^5: `dist/casa/pacPlot`(p); # ----------------------------------------------------------------------------- # parallel plotting of a surface to surface intersection # ----------------------------------------------------------------------------- # sequential 500s plotsetup(x11); p1 := -94*x^2*z-65*x^2*y^3+90*x^4-38*y^3*z^2-46*y*z^3+28*x*z; p2 := 23*x^2*z^2-20*x^2*y^3-7*z^5+4*x*z^4-77*x^2*y*z^2+40*x^3*z^2; `dist/casa/ssiPlot`(p1,p2,[x,y,z]); # ----------------------------------------------------------------------------- # parallel construction of neighborhood graph # ----------------------------------------------------------------------------- c := mkImplAlgSet([y^2-x^9], [x,y]); `dist/casa/neighbGraph`(c); # ----------------------------------------------------------------------------- # session termination # ----------------------------------------------------------------------------- dist[terminate](); # ----------------------------------------------------------------------------- # $Id: EXAMPLES,v 1.5 2001/07/26 05:35:30 schreine Exp $ # -----------------------------------------------------------------------------