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4

I received a prompt response from Wolfram Technical Support: "...there is an option in system setting called 'AssumptionsMaxNonlinearVariables'. This option specifies the maximal number of variables in non-linear inequality assumptions. By default, this option is set as 4. After changing it to 5, the issue is solved" ...

1

On the other hand, we can use DifferentialRootReduce[] on LegendreP[1/2 (-1 + Sqrt[17]), x] to see what linear differential equation is satisfied by it: Operate[FullSimplify, DifferentialRootReduce[LegendreP[1/2 (-1 + Sqrt[17]), x], x]] DifferentialRoot[Function[{y, x}, {-4 y[x] + 2 x y'[x] + (-1 + x^2) y''[x] == 0, y[0] == ...

0

Here I can give a not so intelligent method, for you should judge how many terms in the exponential term. Use the Rule to change back to the require form the code is Exp[x b + y + z] /. {Exp[a_ + b_ + c_] :> Defer[Exp[a] Exp[b] Exp[c]]} then get the result (*Exp[b x] Exp[y] Exp[z]*) I don't know how to made this Rule more intelligent. But sometimes ...

3

It is important to keep in mind that ArcTan[Tan[x]] is not always equal to x. When x is between -Pi/2 and Pi/2, it is valid. So we have In[24]:= ArcTan[Tan[x]] Out[24]= ArcTan[Tan[x]] And In[25]:= FullSimplify[ArcTan[Tan[x]], -Pi/2 < x < Pi/2] Out[25]= x Similarly, it follows that In[26]:= FullSimplify[ArcTan[Cos[x], Sin[x]], ...

2

You can use the ExcludeForms option described in the Simplify documentation. For example, Simplify[{x^2 + 2 x + 1 == 0, 4 x^2 == 0}, ExcludedForms -> {0}] (* returns {(x + 1)^2 == 0, 4 x^2 == 0} *) Alternatively, Simplify[{x^2 + 2 x + 1 == 0, 4 x^2 == 0}, ExcludedForms -> {x^2, 0}] (* returns {1 + 2 x + x^2 == 0, 4 x^2 == 0} *) The actual ...

0

The equality may be used to eliminate one variable of your choice. It may be done by the way used in the @happy fish answer, or by a direct substitution: pol = p + q + r - b; pol /. b -> p + q + r - a (* a *) Have fun!

0

You can use Solve[pol == p + q + r - b && a + b == p + q + r, pol, {b, q, p, r}] or Eliminate[pol == p + q + r - b && a + b == p + q + r, {b, q, p, r}]

1

I think the problem is because the pattern n_/x_ ** y_ doesn't match the expression 1/b ** a. You can see that in the full form: FullForm[1/b ** a] (*Power[NonCommutativeMultiply[b,a],-1]*) FullForm[n/x ** y] (*Times[n,Power[NonCommutativeMultiply[x,y],-1]]*) So this deosn't work Simplify[- (1/a) ** (1/b) + 1/b ** a, Assumptions -> {n_/x_ ** y_ == ...

1

You can use the TargetFunctions option of ComplexExpand[]: FullSimplify[ComplexExpand[(2 (ArcCot[E^(-((I ϕ)/2)) r] + ArcCot[E^((I ϕ)/2) r]))/π, TargetFunctions -> {Re, Im}], r > 1 && -π < ϕ < π] (2 (ArcCot[Sec[ϕ/2] (r + Sin[ϕ/2])] + ArcCot[r Sec[ϕ/2] - Tan[ϕ/2]]))/π One could probably argue for the ...

1

The answer is completely satisfactory. It returns the result in terms of Arg which is always a real number. If look for its imaginary part Im@ComplexExpand[(2 (ArcCot[E^(-((I \[Phi])/2)) r] + ArcCot[E^((I \[Phi])/2) r]))/\[Pi]] 0 So your answer is a Real quantity.

1

$Version (* "10.4.1 for Mac OS X x86 (64-bit) (April 11, 2016)" *) expr = Assuming[{r > 1, -π < ϕ < π, ϕ ∈ Reals}, Sum[ r^-n 4/π Sin[n π/2]/n Cos[n ϕ/2], {n, 1, ∞}]] // FullSimplify expr2 = Assuming[{r > 1, -π < ϕ < π, ϕ ∈ Reals}, expr // ComplexExpand[#, TargetFunctions -> {Re, Im}] & // ... 2 Try this: Sqrt[Im[z1]^2 - 2 Im[z1] Im[z2] + Im[z2]^2 + (Re[z1] - Re[z2])^2] // ComplexExpand // Simplify (* ((z1 - z2)^4)^(1/4) *) Have fun! 3 This is in reaction to a comment: A closer example to my application is this: 1.*10^-22 Sqrt[1.035998097490982*^47 - 6.518057203453232*^45 x]. Rationalize[] does not give a substantial simplification. In this case the scenario is quite different than in the original formulation of the question which would suggest that the numbers involved are still ... 2 Instead of a combination of Rationalize and MantissaExponent, as shown in the answer by JasonB, one can use a combination of FromDigits and RealDigits: Sqrt[3.1 10^45 + x 10^47]/(1 10^22) /. x_Real :> Sign[x]*FromDigits@RealDigits[x] // Simplify$\ \$Sqrt[31 + 1000 x]

2

Hopefully someone can come up with a better way to do this. If I understand correctly, the issue is that Simplify[Sqrt[3 10^45 + x 10^47]/(1 10^22)] gives a nice and short result, with no large powers of 10, (* Sqrt[30 + 1000 x] *) while this Simplify[Sqrt[3.1 10^45 + x 10^47]/(1 10^22)] (* Sqrt[3.1*10^45 + 1.*10^47 x]/10000000000000000000000 *) ...

2

% refers to the last output, which is A (2 x1 + 2 x2) + A B (y1 + y2) in your code; and [[1]] means the first part of that expression in level 1, which is the first part of Plus[A (2 x1 + 2 x2), A B (y1 + y2)], yields A (2 x1 + 2 x2). Similarly the second part is A B (y1 + y2). However, the usage of Simplify here is treating A B (y1 + y2) as an assumption. ...

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