Skip to main content

Questions tagged [assumptions]

Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].

Filter by
Sorted by
Tagged with
2 votes
2 answers
77 views

Simplifying Min with assumptions

Lots of ecological models use Liebig's law of the minimum when multiple essential resources may limit growth. I want to break these equations into the special cases using ...
Chris K's user avatar
  • 20.3k
4 votes
1 answer
145 views

Specifying properties of a function as assumptions

I am trying to simplify expressions involving a function $f: \mathbb C \to \mathbb C$ which satisfies $$f(-z) = -f(z), \quad f(z^*) = f(z)^*, \quad \forall z \in \mathbb C.$$ I do not want to specify ...
ummg's user avatar
  • 143
2 votes
0 answers
108 views

Is there a way to force 'Simplify' to use some assumptions?

First time poster. I have a basic question about 'Simplify'. I am encountering a problem when trying to simplify some algebraic expressions, where I find an unexpected behaviour of the 'Simplify' ...
Johnny Lemmon's user avatar
2 votes
1 answer
48 views

Assuming[a ∈ Reals, Conjugate[a]] fails to invoke assumptions [closed]

Miminmal working example: Assuming[a ∈ Reals, Conjugate[a]] Returns Conjugate[a] instead of ...
Cat Bisque's user avatar
0 votes
0 answers
44 views

Puzzling behavior of `Assumptions` in `Solve`

With Wolfram Language 13.3.0 Engine when solving the following equation: ...
Jos Bergervoet's user avatar
2 votes
1 answer
84 views

Tell Mathematica that the output of a function is a List / Vector

I have a function (Piecewise) that returns a list, e.g.: F[x_] := Piecewise[{{{x^2, x}, x < 0}, {{x, x^2}, x > 0}}, {0, 0}]; I would like to add another list ...
Luis's user avatar
  • 187
4 votes
2 answers
316 views

Why is Assuming[...] ignoring the assumption?

Let's say I want to compute a quantity like $e^{i \pi \vert \vec a \vert}$, and for a certain vector a = {a1,a2,a3} I assume it has length 1, so the quatity would ...
qntdni's user avatar
  • 95
0 votes
0 answers
39 views

Simplify matrix expression with assumptions

I am trying to simplify complex matrix expressions with some assumptions (such as matrix is a rotation matrix). I am failing to do it properly. Find below the simplest example that reproduces the ...
pbp's user avatar
  • 1
1 vote
1 answer
38 views

Check positivity with additional conditions

I am completely new to Mathematica. I would like to check when $$ \frac{1}{2ka}\left(\sqrt{b}x-\frac{z}{\sqrt{b}}\right)^2+\frac{1}{2mb}\left(\sqrt{a}y-\frac{z}{\sqrt{a}}\right)^2+\frac{1}{2c}(bx+ay-z)...
Salamo's user avatar
  • 111
0 votes
1 answer
59 views

Which of the given codes $p1,p2,p3,p4$ is the correct one for imposing assumption in ContourPlot3D using RegionFunction?

I am using ContourPlot3D for the condition f[x_, y_, z_] ==0 assuming that the assumption ...
PhysFan's user avatar
  • 63
1 vote
1 answer
184 views

How to compute this integral $\int_{-\frac c2}^{0} e^{-a \left(\frac{b x^3}{2}-\frac{x^2}{4}\right)} dx $? [closed]

I want to compute this integral: $$ \int_{-\frac c2}^{0} e^{-a \left(\frac{b x^3}{2}-\frac{x^2}{4}\right)} dx \qquad\textstyle{with}\qquad a,b>0 \qquad\textstyle{and}\qquad a,b\in\mathbb{R}$$ The ...
math2021's user avatar
  • 749
1 vote
0 answers
83 views

Why is -1 raised to an odd power different from -1? [closed]

In the following code, shouldn't the result be -1? It doesn't give me anything. Why? Assuming[Element[n, OddQ], (-1)^n] Thank you in advance.
Kώστας Κούδας's user avatar
0 votes
1 answer
80 views

How to plot the given functions $g$ and $h$ with the assumption $f=0$?

I have a constraint f[a_, b_, c_] ==0 with three parameters $0<a,b,c<3$ where ...
math2021's user avatar
  • 749
3 votes
1 answer
151 views

Summation question?

I have following summation that I want to implement using Mathematica: ...
Vayne's user avatar
  • 81
1 vote
0 answers
41 views

How to assume a function is holomorphic?

For example, for a holomorphic function $f(z)=f(x,y)$, it's well know that $\ln |f|$ is harmonic. I want to check it with mathematica with the following code: ...
gaoqiang's user avatar
  • 141
1 vote
3 answers
108 views

Why does assuming f[_] > 0 does not work while Element[f[_], Reals] does?

Refine works with symbols in either way: Refine[Sqrt[x^2], Element[x, Reals]] (* Abs[x] *) Refine[Sqrt[x^2], x > 0] (* x *) ...
JS S's user avatar
  • 121
0 votes
0 answers
25 views

Simplify vector calculus based on component splitting

I am interested in verifying a few Vector Calculus expressions using Mathematica. These expressions are based on splitting a vector field into its transverse components (in the xy- plane) and ...
orlandini's user avatar
1 vote
0 answers
104 views

Integral of complex exponential with assumptions

I feel confident this problem has been posed before but alas I cannot find it. ...
David G. Stork's user avatar
0 votes
2 answers
55 views

Can a redundant condition be removed from a solution?

A solution to this equation: Solve[{(p-x)^2 + (q-y)^2==d, p/q==t}, {p,q}, Reals] has this repetitive condition: $\displaystyle\quad d > \frac{x^2 - 2txy+t^2y^2}{...
scriptfoo's user avatar
  • 211
0 votes
0 answers
66 views

Assuming Refine does not work for all If[] expression part

One simple example as following ...
eason's user avatar
  • 197
0 votes
0 answers
64 views

Solving multiple inequalities

I am new to Mathematica and I want to know if there are solutions to the following 4 coupled inequalities. Note that the inequalities are long and cumbersome with many variables with subscripts (I ...
Monty's user avatar
  • 101
2 votes
2 answers
103 views

Computing a limit with assumptions

This program solves the recurrence for the expected time to extinction of a linear birth and death process with arrival rate A and death rate q A, and then attempts to simplify. ...
florin's user avatar
  • 1,798
4 votes
1 answer
122 views

Questioning Mathematica's Condition Representation: Strange Solution for Integer Variable

I have the following sequence: $$f_n(x)=\left\{\begin{array}{cl} 1 & \text { if } 0 \leq x<\frac{1}{2} \\ 1-(n+1)\left(x-\frac{1}{2}\right) & \text { if } \frac{1}{2} \leq x<\frac{1}{2}+\...
Mark's user avatar
  • 327
4 votes
2 answers
118 views

Why $\texttt{Sqrt}[\textrm{positive value}] > 0$ sometimes simplifies to true, sometimes not

Why this does not evaluate to True: ...
scriptfoo's user avatar
  • 211
2 votes
1 answer
138 views

"Assume whatever makes it easier" command

Is there a shorthand for telling Mathematica to assume things like "everything is a positive real unless specified otherwise" etc? It get's really tedious for expressions with many ...
Gappy Hilmore's user avatar
2 votes
2 answers
114 views

Assumptions in Sum

I am calculating the following ...
mattiav27's user avatar
  • 6,747
2 votes
1 answer
149 views

Evaluation of integral with parameters

I am trying to solve the following integral having two strictly positive parameters: ...
cpcf's user avatar
  • 23
1 vote
1 answer
57 views

Redundant cases from Sum

I am new to Mathematica. I would like to understand why Mathematica returns redundant cases, and whether it is possible to simplify them to the generic case $(n>1)$ that covers everything $(n\ge0)$....
Andras Vanyolos's user avatar
0 votes
0 answers
47 views

Simplify a ComplexExpand with assumptions gives wrong output

Let us define the real and imaginary parts of a specific polynomial root as follows ...
annuk89's user avatar
5 votes
3 answers
125 views

Implementing symmetry assumptions in FullSimplify

I want to symmetrise a long expression, M, that involves a function of 4 arguments, f[u1,u2,d1,d2], and its products (for ...
jms547's user avatar
  • 399
1 vote
1 answer
52 views

A problem with the evaluation of expressions using assumptions through Mathematica

I want to evaluate the expression below, $((2 (a_{01}+2 ya_{02}+x a_{11})^2+(b_{01}+2 y b_{02}+x b_{11})^2) (2 (a_{10}+y a_{11}+2 x a_{20})^2+(b_{10}+y b_{11}+2 x b_{20})^2))$, at $x=-((2 (2 a_{02}a_{...
VH84's user avatar
  • 179
0 votes
1 answer
50 views

Assisting Solve to generate solution to a complicated equation

I have the following Mathematica code: ...
codebpr's user avatar
  • 2,263
1 vote
1 answer
110 views

FunctionPoles with arbitrary undefined function

Good day everyone. I have very simple question about behaviour of the functions FunctionPoles, FunctionMeromorphic e.t.c. Can these functions work properly with undefined functions? For example when I ...
George's user avatar
  • 69
3 votes
1 answer
104 views

Assume asymptotic value in a limit?

Is it possible to give Mathematica a limit about's function at infinity? For example I would like to ...
Nitaa a's user avatar
  • 770
2 votes
2 answers
54 views

Subtituting kronecker deltas for products in simplification

I have a problem where I have some vector, $a = (a_1, a_2, \ldots, a_n)^T$ that I want to have a Kronecker delta multiplication rule, $a[i]a[j] = \delta_{ij}$ (these are basically basis vectors, but ...
Joshua Schraiber's user avatar
1 vote
0 answers
30 views

Making an "unsafe" simplify that ignores the validity conditions of simplifications

Mathematica will never make assumptions you don't tell it to make, and will state all conditions under which the answers it gives are valid. While this is overall a good thing, this often leads to ...
eyeballfrog's user avatar
0 votes
0 answers
62 views

Refine not able to simplify for PositiveReals

If I type in Mathematica Refine[d^2 == a^2, {a ∈ PositiveReals, d ∈ PositiveReals}] I get d^2 == a^2 Why don't I get ...
Kelthar's user avatar
0 votes
1 answer
110 views

How to tell Mathematica to solve an equation assuming all solutions are non-negative reals? [closed]

The title. I have a system of 6 equations that I want to solve. The system is non-linear. I want to solve it, but I just want Mathematica to give me solutions that are non-negative reals (so no ...
Granger Obliviate's user avatar
1 vote
1 answer
185 views

How can I force Mathematica to calculate this integral?

I have the following expression. I realize Mathematica has a little bit of trouble with Abs[] as it assumes variables to be complex and etc., but I am trying to compute an integral and it just keeps ...
Granger Obliviate's user avatar
1 vote
0 answers
69 views

Finding the (symbolic) eigenvalues of a matrix with some assumption

I have the following 3$\times$3 symmetric matrix with symbolic entries. Meff = \begin{array}{ccc} 2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta $11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
neuoscman's user avatar
1 vote
0 answers
46 views

Enforcing the continuity of solutions throughout the whole range of variable in NDSolve, when there are multiple solutions

I am solving differential equations numerically by using NDSolve. Let's say that the function that I want to obtain is f[t]. Then, it turns out that my differential equation is a sextic polynomial of ...
Youngsub Yoon's user avatar
0 votes
0 answers
89 views

Why do I get different results for this complex line integral?

I want to compute line integral of $f(z) = \frac{1}{z(z-1)^{n+1}}$ over a closed curve $\gamma: t \mapsto 1 + \frac{1}{2} e^{i t}, t \in [0,2\pi]$ in the complex plane in two different ways but the ...
Physor's user avatar
  • 153
5 votes
2 answers
271 views

How can I make assumptions in NDSolve?

Suppose I try to solve the following differential equation numerically. (My example is much more complicated, but for simplicity, let's consider this example.) ...
Youngsub Yoon's user avatar
1 vote
0 answers
37 views

Is there a nice way to deal with sets in an abstract/symbolic way?

For instance, if I wanted to declare $A$ to be the set of all finite subsets of $\mathbb{Z}$, and declare $B$ to be a set comprising all finite subsets of $\mathbb{Z^{-}}$, and then declare $C$ to be ...
Trev's user avatar
  • 763
0 votes
0 answers
47 views

Double variable integration unable to prove that integration limits are real

I have simple question regarding double integrating a function. J*Integrate[Integrate[Cos[ArcTan[Sqrt[(x - a)^2 + (y - b)^2]/L]], {b, -b, b}], {a, -a,a}] The error ...
M. Dogan's user avatar
4 votes
1 answer
89 views

Simplify and Assumptions

Am I missing something here? Thanks for any help! SN
Sébastien Neukirch's user avatar
1 vote
0 answers
36 views

Limitations of Assumptions

Why don't Simplify[x[2, 1] < x[1, 3], Assumptions -> {x[a_, b_] > x[c_, d_] /; a > b && c < d}] or ...
user46831's user avatar
  • 643
0 votes
1 answer
64 views

Integral behaviour?

I'm trying to find a standard integral, which shows itself up in general relativity (proper distance in Schwarzschild metric). For example in this video. The integral is shown as where $r_s< r$ ...
Nitaa a's user avatar
  • 770
3 votes
1 answer
249 views

Why does the assuming not work as expected?

Why does this not work? I expect the output would be something like 1/s*e^-(sT). ...
internet's user avatar
  • 593
0 votes
1 answer
72 views

What is the most efficient/optimal way to simplify the given function? Does the given code need more assumptions?

I have a very long function for $\{x,b\}\in\mathbb{R}$ and $n=\{1,2,3,4,5,6,7,8,9,10\}$; here, I have only mentioned a short part of that. The function is a sum of the complex exponentials (a picture ...
charmin's user avatar
  • 1,159

1
2 3 4 5
11