#3466 solve does not find all solutions of a nonlinear system

[M. Stanev]

The system [x^2+xy+y^2=12, x+y+x^2y^2=12]
has 8 solutions / the solution [x=-2, y=-2] is counted 2 times/
They are obvious when the the two graphs are plotted
simultaneously with the command
implicit_plot

I use the substitution u=x+y, v=x*y to solve the system
by hand.

However, the command
solve([x^2+xy+y^2=12,x+y+x^2y^2=12],[x,y]);
returns a list of 5 solutions / the solution [x=-2, y=-2] is one of them
=> we obtain 6 solutions /.

So, the problem is that maxima knows nothing about the remaining two solutions.

wxbug_report()
wxMaxima version: 16.4.2
Maxima version: 5.38.1
Maxima build date: 2016-10-19 00:27:24
Host type: x86_64-suse-linux-gnu
System type:
gcc -g -fmessage-length=0 -grecord-gcc-switches -O2 -Wall -D_FORTIFY_SOURCE=2 -fstack-protector -funwind-tables -fasynchronous-unwind-tables -g -fno-strict-aliasing -fPIC -pipe -fno-gcse -g -O2 -W -Wswitch -Wcomment -Wpointer-arith -Wimplicit -Wreturn-type -Wmissing-declarations -Wno-sign-compare -Wno-format-nonliteral -O -falign-functions=4 -D_LARGEFILE64_SOURCE -D_FILE_OFFSET_BITS=64 -D_GNU_SOURCE -Wno-unused -Wno-uninitialized -DSAFETY=3 -O -DENABLE_UNICODE -DDYNAMIC_FFI -DDYNAMIC_MODULES -I. /usr/lib64/libreadline.so -lncurses -ldl /usr/lib64/libavcall.a /usr/lib64/libcallback.a -L/usr/lib64 -lsigsegv libgnu_cl.a
SAFETY=3 TYPECODES WIDE_HARD SPVW_BLOCKS SPVW_MIXED TRIVIALMAP_MEMORY
libsigsegv 2.10
libreadline 6.3
libffcall 1.11 GNU C 4.8.5 X86_64
Lisp implementation type: CLISP
Lisp implementation version: 2.49 (2010-07-07) (built on cloud112 [127.0.0.1])

[Hisham Sueyllam]

This is not a bug. You only need to load(grobner); then define eqs:[x^2+xy+y^2-12,x+y+X^2y^2-12] and the vars:[x,y]then call poly_reduced_grobner(eqs,vars); then algsys(%,vars);and you will have all 7 solutions with the repeated one -2, -2 counted only once.
hisham...

On Monday, October 1, 2018, 9:54:36 PM GMT+2, M. Stanev <mstanev@users.sourceforge.net> wrote:

[bugs:#3466] solve does not find all solutions of a nonlinear system

Status: open
Group: None
Labels: solve
Created: Mon Oct 01, 2018 07:54 PM UTC by M. Stanev
Last Updated: Mon Oct 01, 2018 07:54 PM UTC
Owner: nobody

The system [x^2+xy+y^2=12, x+y+x^2y^2=12]
has 8 solutions / the solution [x=-2, y=-2] is counted 2 times/
They are obvious when the the two graphs are plotted
simultaneously with the command
implicit_plot

I use the substitution u=x+y, v=x*y to solve the system
by hand.

However, the command
solve([x^2+xy+y^2=12,x+y+x^2y^2=12],[x,y]);
returns a list of 5 solutions / the solution [x=-2, y=-2] is one of them
=> we obtain 6 solutions /.

So, the problem is that maxima knows nothing about the remaining two solutions.

wxbug_report()
wxMaxima version: 16.4.2
Maxima version: 5.38.1
Maxima build date: 2016-10-19 00:27:24
Host type: x86_64-suse-linux-gnu
System type:
gcc -g -fmessage-length=0 -grecord-gcc-switches -O2 -Wall -D_FORTIFY_SOURCE=2 -fstack-protector -funwind-tables -fasynchronous-unwind-tables -g -fno-strict-aliasing -fPIC -pipe -fno-gcse -g -O2 -W -Wswitch -Wcomment -Wpointer-arith -Wimplicit -Wreturn-type -Wmissing-declarations -Wno-sign-compare -Wno-format-nonliteral -O -falign-functions=4 -D_LARGEFILE64_SOURCE -D_FILE_OFFSET_BITS=64 -D_GNU_SOURCE -Wno-unused -Wno-uninitialized -DSAFETY=3 -O -DENABLE_UNICODE -DDYNAMIC_FFI -DDYNAMIC_MODULES -I. /usr/lib64/libreadline.so -lncurses -ldl /usr/lib64/libavcall.a /usr/lib64/libcallback.a -L/usr/lib64 -lsigsegv libgnu_cl.a
SAFETY=3 TYPECODES WIDE_HARD SPVW_BLOCKS SPVW_MIXED TRIVIALMAP_MEMORY
libsigsegv 2.10
libreadline 6.3
libffcall 1.11 GNU C 4.8.5 X86_64
Lisp implementation type: CLISP
Lisp implementation version: 2.49 (2010-07-07) (built on cloud112 [127.0.0.1])

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[M. Stanev]

The problem was that the command poly_reduced_grobner(eqs,vars); had never worked for me.
(even after waiting for about 2 hours).

A couple hours ago I installed Maxima 5.42.0 and wxMaxima 18.02.0.
The command load(grobner) failed and
the command solve([x^2+xy+y^2-12, x+y+x^2y^2-12],[x,y]);
returned the desired answer with all solutions.

Thank you!

wxMaxima version: 18.02.0
Maxima version: 5.42.0
Maxima build date: 2018-10-06 14:34:08
Host type: x86_64-unknown-linux-gnu
System type:
gcc -g -fmessage-length=0 -grecord-gcc-switches -O2 -Wall -D_FORTIFY_SOURCE=2 -fstack-protector -funwind-tables -fasynchronous-unwind-tables -g -fno-strict-aliasing -fPIC -pipe -fno-gcse -g -O2 -W -Wswitch -Wcomment -Wpointer-arith -Wimplicit -Wreturn-type -Wmissing-declarations -Wno-sign-compare -Wno-format-nonliteral -O -falign-functions=4 -D_LARGEFILE64_SOURCE -D_FILE_OFFSET_BITS=64 -D_GNU_SOURCE -Wno-unused -Wno-uninitialized -DSAFETY=3 -O -DENABLE_UNICODE -DDYNAMIC_FFI -DDYNAMIC_MODULES -I. /usr/lib64/libreadline.so -lncurses -ldl /usr/lib64/libavcall.a /usr/lib64/libcallback.a -L/usr/lib64 -lsigsegv libgnu_cl.a
SAFETY=3 TYPECODES WIDE_HARD SPVW_BLOCKS SPVW_MIXED TRIVIALMAP_MEMORY
libsigsegv 2.10
libreadline 6.3
libffcall 1.11 GNU C 4.8.5 X86_64
Lisp implementation type: CLISP
Lisp implementation version: 2.49 (2010-07-07) (built 3685811133) (memory 3747814450)
wxMaxima's idea of the directory layout is:
Icon dir: /usr/share/wxMaxima
User configuration dir: /home/martin/
Help dir: /usr/share/doc/wxmaxima
Maxima lisp dir: /usr/local/share/maxima//5.42.0