Remove vacuous solutions from solve

[ppurka]

Sometimes solve and its variants tend to report vacuous solutions. A recent one from ask.sagemath is the following:

sage: x,y = var('x,y')
sage: solve([x^2*y^2 <= x^2*y, x^2*y^2 > x^2*y],[x,y])
[[x == 0, 1 < y, 0 != 0], [x == 0, y < 0, 0 != 0]]

Shouldn't we remove these meaningless solutions? The attached patch contains a potential solution. If it seems reasonable, then similar changes could be introduced in solve_ineq.

The output of the above command after this patch is as expected:

sage: x,y = var('x,y')
sage: solve([x^2*y^2 <= x^2*y, x^2*y^2 > x^2*y],[x,y])
[]

---

If you can translate this to maxima proper, please feel free to do so and submit a patch upstream.

---

Workaround: call maxima_calculus("domain: real") before solve (see comment 12).

CC: @kcrisman @jondo

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/14229

[ppurka]

Apply to devel/sage

[ppurka]

comment:1

Attachment: trac_14229-remove_vacuous_solutions.patch.gz

[ppurka]

Description changed:

--- 
+++ 
@@ -6,4 +6,4 @@
 [[x == 0, 1 < y, 0 != 0], [x == 0, y < 0, 0 != 0]]
 ```
 
-Shouldn't we remove these meaningless solutions?
+Shouldn't we remove these meaningless solutions? The attached patch contains a potential solution. If it seems reasonable, then similar changes could be introduced in `solve_ineq`.

[ppurka]

Description changed:

--- 
+++ 
@@ -7,3 +7,11 @@
 ```
 
 Shouldn't we remove these meaningless solutions? The attached patch contains a potential solution. If it seems reasonable, then similar changes could be introduced in `solve_ineq`.
+
+The output of the above command after this patch is as expected:
+
+```
+sage: x,y = var('x,y')
+sage: solve([x^2*y^2 <= x^2*y, x^2*y^2 > x^2*y],[x,y])
+[]
+```

[nbruin]

comment:5

This kind of change should really be made to maxima, not to sage's postprocessing of what maxima returns.

[ppurka]

Work Issues: port to upstream

[ppurka]

comment:6

If someone knows how to translate this to maxima, please feel free to put this upstream. Thanks! [ I can not spend time in learning maxima right now. :( ]

[ppurka]

Description changed:

--- 
+++ 
@@ -15,3 +15,7 @@
 sage: solve([x^2*y^2 <= x^2*y, x^2*y^2 > x^2*y],[x,y])
 []
 ```
+
+---
+
+If you can translate this to maxima proper, please feel free to do so and submit a patch upstream.