Simplifying a combination of atomic inequalities

[jondo]

How can I simplify

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(x == 0 and 1 < y and 0 != 0) or (x == 0 and y < 0 and 0 != 0)

(from Sage trac) to "false" (or find the empty solution set)?

I have had a look at the pdf manual, but did not get it.

The following does not work:

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giac: simplify((x == 0 and 1 < y and 0 != 0) or (x == 0 and y < 0 and 0 != 0))
0
giac: solve((x == 0 and 1 < y and 0 != 0) or (x == 0 and y < 0 and 0 != 0),[x,y])
NaN

By the way, the link to the online reference is broken on http://www-fourier.ujf-grenoble.fr/~par ... c.html#doc.

[jondo]

Also, can Giac somehow solve the original system of inequalities?

"solve" does not work:

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Xcas: solve([x^2*y^2 <= x^2*y, x^2*y^2 > x^2*y],[x,y])
"[x,(x^2*y^2)<=(x^2*y),(x^2*y^2)>(x^2*y)] is not rational w.r.t. x Error: Bad Argument Value"

[jondo]

Somehow similar:

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Xcas: solve([abs(x-1) > 1, abs(x-2) > 1],x)
list[0>x,x>3]

works fine. But if I want to compute the solutions separately:

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Xcas: s1:=solve(abs(x-1) > 1,x) 
list[0>x,x>2]
Xcas: s2:=solve(abs(x-2) > 1,x) 
list[1>x,x>3]

, how can I intersect s1 and s2?

[parisse]

Sorry, there is currently nothing in giac for that.