Questions tagged [assumptions]
Questions about the function Assuming[], the $Assumptions system variable, and the Assumptions option of functions such as Simplify[] and Integrate[].
535
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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:
...
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3
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101
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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 *)
...
- 31
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0
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23
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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 ...
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0
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98
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Integral of complex exponential with assumptions
I feel confident this problem has been posed before but alas I cannot find it.
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2
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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}{...
- 201
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64
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0
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63
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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 ...
- 101
2
votes
2
answers
97
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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.
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- 1,642
4
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1
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119
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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}+\...
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2
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118
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Why $\texttt{Sqrt}[\textrm{positive value}] > 0$ sometimes simplifies to true, sometimes not
Why this does not evaluate to True:
...
- 201
2
votes
1
answer
127
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"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 ...
- 1,243
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2
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93
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2
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1
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143
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Evaluation of integral with parameters
I am trying to solve the following integral having two strictly positive parameters:
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1
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55
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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)$....
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0
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0
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47
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Simplify a ComplexExpand with assumptions gives wrong output
Let us define the real and imaginary parts of a specific polynomial root as follows
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0
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0
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19
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Specifying and assigning arguments of a function to be real
I have the following complex matrix that I wish to integrate (element-by-element)
...
- 385
5
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3
answers
116
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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 ...
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1
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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_{...
- 179
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1
answer
46
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Assisting Solve to generate solution to a complicated equation
I have the following Mathematica code:
...
- 899
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1
answer
101
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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 ...
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1
answer
88
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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
...
- 698
2
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2
answers
50
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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 ...
1
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0
answers
27
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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 ...
- 111
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0
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Compute symbolic identities for FourierTransform
Mathematica computes some of the identities for Fourier transforms for an arbitrary function f[t] directly, for example:
FourierTransform[f'[t], t, w]
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- 40k
0
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0
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62
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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 ...
- 1
0
votes
1
answer
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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 ...
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1
answer
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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 ...
1
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0
answers
56
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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{...
- 11
1
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0
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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 ...
- 169
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0
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81
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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 ...
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2
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238
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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.)
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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 ...
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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 ...
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88
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1
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0
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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
...
- 633
0
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1
answer
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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$ ...
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3
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1
answer
178
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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).
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1
answer
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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 ...
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1
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How to use Assuming and With together
(I am sorry for the ASCII form, I use the free WolframEngine which works in text mode.)
I have these assumptions ...
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1
answer
69
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0
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0
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45
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Mathematica FullSimplify becomes less simplified with more specific assumptions?
As far as I always understood, Mathematica always assumes an expression to represent the most general state. For example, a variable is usually assumed to be Complex...
- 1,357
2
votes
2
answers
100
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Pattern or ForAll statment in Assumptions
I would like to simplify an expression like
$\sum _{i=1}^k \sqrt{a_i^2}$, with the condition $\forall _{i\in \mathbb{Z}_{>\, 0}}a_i\in \mathbb{R}_{>\, 0}$ and with $k$ being undefined, which ...
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1
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Need help with Assumptions for an integral
I want to solve this Log, Integrate[2a Log[-a+((A0 + (y-y1)²)^½, {y1, 0,b}]
But Mathematica only gives me long conditional expressions or imaginary numbers. I (my thinking which can be wrong) assume I ...
- 1
5
votes
3
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204
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$Assumptions = _ ∈ Reals results in incorrect simplification of ConjugateTranspose[..]
The linear combination $Q$ of two Hermitian matrices $A^\dagger = A, B^\dagger = B$ with real coefficients $m,n \in \mathbb{R}$, i.e. $Q = m A + n B$ is itself a Hermitian matrix $Q^\dagger = Q$.
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2
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1
answer
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Struggling to get Solve to accept assumptions
I can't get Solve to solve the following two equations under the appropriate assumptions.
When I enter
...
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1
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Assuming one variable is greater than another variable
I want to add the assumption that M>m, but I am not sure how to do that.
I tried
Assuming[M > m, M > m]
But this ...
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2
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Making a substitution within a typeset integral
This question derives directly from this one, but concerns instead a different matter... one related to display format.
This integral
$$I = \int\limits_2^4 \frac{\sqrt{\log (9-x)}}{\sqrt{\log (9-x)}+\...
- 40k
8
votes
1
answer
226
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Why Mathematica is treating the product of (specified) real variable as complex?
For the given matrix
...
- 539
4
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1
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54
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Proper usage of Assuming statement
I want to evaluate a command under an assumption, and thought Assuming was the right way to go. Suppose we want to calculate a Matrix rank. Following the second ...
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0
answers
34
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Put an initial condition on some parameter
Good morning,
I'm new in the world of Mathematica, so I'm sorry if my question isn't very relevant.
I'm trying to solve a system of 5 equations withs many parameters. To be clear, I will hit the core ...
- 101