solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] -> { [x,0] [0, y] }
09-21-2016, 02:22 PM
Post: #1
 compsystems Senior Member Posts: 1,341 Joined: Dec 2013
solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] -> { [x,0] [0, y] }
Hello
HP-Prime
solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] returns
{[x,0]} it means x=x, x takes any parameter & y = 0

now inverting variables {x, y} -> {y, x}
solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{y, x}) [Enter] returns
{[y,0]} it means y=y, y takes any parameter & x = 0

Why the CAS not return the full answer?

solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] ->
{ [x,0] [0, y] } -> (x = x and y = 0) or (x = 0 and y = y)

or

solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{y, x}) [Enter] ->
{ [0,x] [y, 0] } -> (y = 0 and x = x) or (y = y and y = 0)

within a program reverse variables the logic of the code becomes more complicated

The CAS of ti68K calculators (ti89/nspire), if return the complete solution =)
solve( 2*x^2*y^2= 0 and 2*y^2*x^2 = 0 ,{x,y}) [Enter] returns
(x = x and y = 0) or (x = 0 and y = y)
09-21-2016, 05:37 PM (This post was last modified: 09-21-2016 05:39 PM by parisse.)
Post: #2
 parisse Senior Member Posts: 1,243 Joined: Dec 2013
RE: solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] -> { [x,0] [0, y] }
The reason is the same as for solve(x*y,[x,y]) or solve(x*y,x), no special case for y=0. If your system has more unknowns than equation (after gbasis computation), it is solved with respect to the last unknown(s) it depends on, regarding the first "unknown(s)" as parameters, and solve happens in the generic situation.
09-21-2016, 06:59 PM
Post: #3
 John P Member Posts: 209 Joined: Dec 2013
RE: solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] -> { [x,0] [0, y] }
(09-21-2016 05:37 PM)parisse Wrote:  The reason is the same as for solve(x*y,[x,y]) or solve(x*y,x), no special case for y=0. If your system has more unknowns than equation (after gbasis computation), it is solved with respect to the last unknown(s) it depends on, regarding the first "unknown(s)" as parameters, and solve happens in the generic situation.

Sir,
Could you direct me to the place where I can download the latest manual(s) for XCAS, English and/or French it doesn't matter.
Thank you.
09-22-2016, 06:34 AM
Post: #4
 parisse Senior Member Posts: 1,243 Joined: Dec 2013
RE: solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] -> { [x,0] [0, y] }
09-22-2016, 03:59 PM
Post: #5
 John P Member Posts: 209 Joined: Dec 2013
RE: solve({ 2*x^2*y^2 = 0,2*y^2*x^2 = 0},{x,y}) [Enter] -> { [x,0] [0, y] }
(09-22-2016 06:34 AM)parisse Wrote:  French http://www-fourier.ujf-grenoble.fr/~pari...r.html#doc
English http://www-fourier.ujf-grenoble.fr/~pari...c.html#doc
Thank you.
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