Revision history [back]

I would not agree with you that these solutions are 'wrong'. They are just presented in a very user unfriendly way. The 1st one, i.e.:

[x == 1, -2 > 0]

definitely is a solution - its just of measure zero, since

sage: -2>0
False

so, it is not 'wrong' as you state - it is just 'useless' ;) The other solution is also perfectly ok since

sage: bool(-(t - 2)^2 + 2*(t - 2)*t - t^2 + 6)
True

so, the solution you want is

x == (t - 2)/t

which I think is ok ..... however I would definetely agree with you that

<math xmlns="http://www.w3.org/1998/Math/MathML" mathematica:form="StandardForm" xmlns:mathematica="http://www.wolfram.com/XML/"> <mrow> <mrow> <mrow> <mi>f</mi> <mo>[</mo> <mrow> <mi>x_</mi> <mo>,</mo> <mi>t_</mi> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mrow> <mrow> <mi>Exp</mi> <mo>[</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>t</mi> </mrow> <mo>]</mo> </mrow> <mo>⁢</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <mo>^</mo> <mn>2</mn> </mrow> </mrow> </mrow> <mo>;</mo> </mrow> </math> <math xmlns="http://www.w3.org/1998/Math/MathML" mathematica:form="StandardForm" xmlns:mathematica="http://www.wolfram.com/XML/"> <mrow> <mi>FullSimplify</mi> <mo>[</mo> <mrow> <mi>Solve</mi> <mo>[</mo> <mrow> <mrow> <mo>{</mo> <mrow> <mrow> <mrow> <mi>D</mi> <mo>[</mo> <mrow> <mrow> <mi>f</mi> <mo>[</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> <mo>]</mo> </mrow> <mo>,</mo> <mi>x</mi> </mrow> <mo>]</mo> </mrow> <mo>⩵</mo> <mn>0</mn> </mrow> <mtext> </mtext> <mo>,</mo> <mtext> </mtext> <mrow> <mrow> <mi>D</mi> <mo>[</mo> <mrow> <mrow> <mi>f</mi> <mo>[</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>,</mo> <mn>2</mn> </mrow> <mo>}</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo><</mo> <mn>0</mn> </mrow> <mo>,</mo> <mrow> <mi>x</mi> <mo>∈</mo> <mi>Reals</mi> </mrow> <mo>,</mo> <mrow> <mi>t</mi> <mo>∈</mo> <mi>Reals</mi> </mrow> </mrow> <mo>}</mo> </mrow> <mo>,</mo> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>t</mi> </mrow> <mo>}</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>]</mo> </mrow> </math> <math xmlns="http://www.w3.org/1998/Math/MathML" mathematica:form="StandardForm" xmlns:mathematica="http://www.wolfram.com/XML/"> <mrow> <mo>{</mo> <mrow> <mo>{</mo> <mrow> <mi>t</mi> <semantics> <mo>→</mo> <annotation encoding="Mathematica">"->"</annotation> </semantics> <mrow> <mi>ConditionalExpression</mi> <mo>[</mo> <mrow> <mrow> <mo>-</mo> <mfrac> <mn>2</mn> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>+</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>t</mi> <mo>|</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mo>∈</mo> <mi>Reals</mi> </mrow> </mrow> <mo>]</mo> </mrow> </mrow> <mo>}</mo> </mrow> <mo>}</mo> </mrow> </math>

from a well known competitor is far more user friendly

I would not agree with you that these solutions are 'wrong'. They are just presented in a very user unfriendly way. The 1st one, i.e.:

[x == 1, -2 > 0]

definitely is a solution - ~~its~~ it just specifies a range of measure zero, since

sage: -2>0
False

so, it is not 'wrong' as you state - it is just ~~'useless'~~ 'totally useless' ;) The other solution is also perfectly ok since

sage: bool(-(t - 2)^2 + 2*(t - 2)*t - t^2 + 6)
True

so, the solution you want is

x == (t - 2)/t

which I think is ok ..... however I would definetely agree with you that

In[1]:= f[x_, t_] = Exp[x t] (x - 1)^2;
In[2]:= Solve[{D[f[x, t], x] == 0 , D[f[x, t], {x, 2}] < 0, {x, t}]
Out[2]= {{t -> ConditionalExpression[-(2/(-1 + x)), (t | x) \[Element] Reals]}}

from a well known competitor is far more user friendly