Questions tagged [products]
Questions about the use of `Product`, `NProduct`, and other types of multiplication, like `Dot`.
100
questions
5
votes
2
answers
192
views
How to type following expression in Mathematica
I want to eneter following expression in mathematica
$$\prod_a^3 \prod_{b\neq a}^3 \frac{x(a)}{b-a}$$
How is this extra condition in product entered in Mathematica?
Without the restriction, I would ...
- 357
1
vote
3
answers
57
views
Digits product and an iteration process
I would like to create a code which gives me the square of the product of the digits of a number, with the only rule that if a number has a 0, then it doesn't count in the product (for example, if the ...
- 67
0
votes
1
answer
90
views
dot product and norm [closed]
Can you solve the following problem in mathematica program? Thank you.
Let x=(x1,x2,x3),y=(y1,y2,y3) and ⟨x,y⟩=x1y1+2x2y2+x3y3 be an inner product in a three-dimensional real vector space.
Define the ...
- 13
4
votes
1
answer
134
views
Numeric evaluation of a matrix product integral
Working on a problem in quantum mechanics, I rediscovered a notion of a product integral, which I was not familiar with before. In a simple case, when the integrand is a real-valued scalar function, ...
- 6,846
5
votes
2
answers
222
views
How to handle excluded values in a summation or product in Mathematica
I want help to writ that on Wolfram Mathematica :
How can I handle the $i \ne j$ part?
2
votes
0
answers
73
views
dot product of one thousand matrices [closed]
I have a time dependent matrix. In a thousand different times with the same time intervals I get the values of the matrices. Now, how can I DOT Product these thousand matrices in time order??
0
votes
1
answer
54
views
Partial derivative of n-variables product [duplicate]
I am new to Mathematica. I would like to calculate the partial derivative of the product,
$\frac{\partial}{\partial x_{j}} y \prod _{i=1}^{n}x_{i}^3=\frac{3}{x_j} y \prod_{i=1}^nx_i^3$, where $1 < ...
- 123
1
vote
0
answers
57
views
How to create this list
Suppose I have two kinds of operators $a[i,j],a^\dagger[i,j]$ where i is a non-negative integer and $j=\pm 1$, I want to create a list containing all possible products of
$ a^{(\dagger)}[x_1,j_1]a^{(\...
- 51
2
votes
2
answers
86
views
Overwrite a tensor product notation a_\[TensorProduct]b_ := KroneckerProduct[a, b]
I noticed that the definition of KroneckerProduct and
For example
TensorProduct[({
{0, 1},
{1, 0}
}), ({
{0, 1},
{1, 0}
})]
Output: {{{{0,0},{0,0}}...
- 823
2
votes
1
answer
145
views
define edge set of a graph
I want to define a graph in Mathematica which its vertex set is cartesian product of two sets. I define the vertex set by Tuple[]
but two vertices are adjacent if and only if the intersection of the ...
- 33
1
vote
2
answers
53
views
Transform a Matrix as an expression
If I have a matrix that I know it can be written as (xi.xi)*KroneckerProduct(H,xi), where xi and H are vectors. Is there a way to obtain this expression from a given matrix?
- 41
1
vote
1
answer
47
views
Guess the next number formula [closed]
I have a sequence of numbers such as {1,2,4,8,16}
The goal is to create a polynomial f(x) such that:
f(0)=1, f(1)=2, f(2)=4, f(n)=nth item on the list
I found this function which claims to do exactly ...
- 676
0
votes
0
answers
63
views
Cancel common factors in symbolic product
Suppose I have the following function
G[n_, k_] := Product[g[n + i]/g[i], {i, 0, k}]
where $n,k$ are assumed to be natural numbers and $g$ is a nonzero symbolic ...
- 121
5
votes
2
answers
285
views
How to plot multifactorial function?
The multifactorial function can be extended to the reals (see TheSimpliFire answer) like so:
It follows that we can extend the multifactorial function to the reals ...
- 11.1k
1
vote
3
answers
163
views
How to factorize $f(x,y)$ into $f_1(x)f_2(y)$? [duplicate]
Suppose we have a real function $f:\mathbb R^2 \rightarrow \mathbb R$ and we would like to know if this function factorizes into $f(x,y)=f_1(x)f_2(y)$ for some real functions $f_1,f_2$. Is there an ...
- 125
1
vote
2
answers
48
views
Multiplication with custom notation
I would like to compute the product
$$(Es+r_{13})(F_{13}s)(F_{3}s+r_{3})(F_{2}s+r_{2})(F_{12}s+r_{12})(F_{1}s+r_{1})(F_{23}s+r_{23})$$
where $E$, $F_i$, and $r_i$ represent arbitrary numbers whose ...
- 113
0
votes
0
answers
40
views
The command Total sums the entries of a list, is there a comparable command for the product of entries of a list? [duplicate]
I recently just found out about the command Total that gives the sum of a list. Was wondering whether there's an analogue that gives the product of the entries of a list? I see that there is the ...
- 2,215
0
votes
0
answers
75
views
How To Define An Outer Product (in xAct)?
I am working with xAct / xCoba / xTras and I would like to construct a matrix out of a vector.
So, I have a vector V on a manifold ...
- 151
2
votes
1
answer
95
views
Plotting list data of cross product of field vectors
I have some experimental data points of electric Ey(t, value) and magnetic field Hz(t, value). I am trying to calculate the ...
- 981
1
vote
0
answers
446
views
How to prove the Grassmann identity in vector form? [closed]
I am given the following question: Show that for all vectors a,b,c the Grass-mann identity holds:
$$ a\times (b\times c)\text {=} (a\cdot c)b - (a\cdot b)c $$
I have tried entering the above identity ...
- 111
1
vote
0
answers
111
views
partial derivative of sum and product
I would like to compute $\frac{\partial}{\partial f_i} \prod_{j=1}^N f_j$, where $1\le i\le N$. By typing e.g.
F[f_] = Product[f[i], {i, 1, N}]
D[F[f], f[1]]
...
- 133
1
vote
1
answer
70
views
Need to verify strange behavior with Product[]
I'm running 12.1.0.0 on MacOS X x86 (64-bit). The expression
Product[1 - 1/n^5, {n, 2, Infinity}]
yields 0 as output, which is ...
- 1,917
2
votes
0
answers
49
views
How to calculate the numerical integration of the product of two entries of an exponential matrix? [closed]
Lets define a $6\times6$ matrix $M(t)$ with entries $m_{ij}$ as
...
- 731
5
votes
1
answer
102
views
How can I tell `Dot` to behave automatically linear?
I would like the number $a$ to be taken out:
...
- 155
10
votes
0
answers
230
views
Why is Product[1 + 1/k^5, {k, 1, Infinity}] equal to zero in 12.1?
In all versions up to 12.0 it is
...
- 2,444
1
vote
1
answer
38
views
Multiplying two expressions with a specific function, efficiently
Paraphrasing, the problem I am trying to solve is the following. I am given two "matrix valued" sums
...
- 180
3
votes
1
answer
62
views
Using the elements of one Matrix to form a new Matrix with specified rules
Given a matrix [a], how to get matrices [b] and [c] based on the following two rules?
rule [a]->[b]: Strike out corresponding term in [a] and take product
of the remaining two terms in the same ...
- 663
8
votes
2
answers
209
views
How to simplify Sum's and Product's of arbitrary length?
I would expect
Sum[Subscript[x,i], {i, 1, n}] + Sum[-Subscript[x,i], {i, 1, n}]
and
...
- 83
4
votes
3
answers
406
views
Smoother ways for setting up a Product function with j=0 and j != i
I want to implement a Product function, particularly the Lagrange polynomial
$\ell_{i}(x)=\prod_{j=0 \atop j \neq i}^{n} \frac{x-x_{j}}{x_{i}-x_{j}}$
Are there ways to implement the "not equal" ...
- 65
9
votes
2
answers
194
views
Closed form of product of Gamma function
Mathematica
recognizes this closed form
\begin{align}
\prod_{k=1}^{n-1}\sin(\pi k/n)
&=
2^{1-n}\,n
\end{align}
just fine:
but fails
on this one
despite that this expression also has a known ...
- 193
1
vote
0
answers
88
views
Simplifying the dot product [closed]
Why does the code
D[x.x, x] /. {1. x -> x, x .1 -> x}
gives 1.x+x.1,
while
...
- 641
1
vote
0
answers
60
views
How to evaluate an expression [closed]
I have a 3-dimensional array of numbers say A. I want to evaluate the following expression.
$\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...
- 111
11
votes
1
answer
254
views
Why is this product equal to zero, when the correct result is 2+GoldenRatio?
Consider the following product
$$
\prod _{k=2}^{\infty } \frac{1}{1-\frac{\left(\frac{1}{2} \left(\sqrt{5}-1\right)\right)^k}{1-\left(\frac{1}{2} \left(\sqrt{5}-1\right)\right)^{2 k}}}$$
Mathematica ...
- 2,444
1
vote
1
answer
142
views
How to multiply the elements of each site of tensor products to each other while using symbolic representation?
If I have, say three sites in a symbolic operator which is of the form A = a⊗1⊗c and I want it to act on another operator B = a1⊗b⊗1 in order to find the commutator A.B - B....
- 13
1
vote
2
answers
99
views
2
votes
1
answer
80
views
Product from max to min [closed]
Product[f[i], {i, 1, 4}]
gives us
f[1] f[2] f[3] f[4]
Is there any way I can take the product it will give something ...
- 177
1
vote
1
answer
147
views
Series of a product of series
I am writing a code where I have to multiply large series truncated at some order, say 100.
As a result I want again a series up to order 100, and I want to get it in the fastest way.
I have tried a ...
- 415
11
votes
1
answer
251
views
How to calculate $\prod\limits_{p}\frac{p^2+1}{p^2-1}$?
When I input
$$
\prod _{p=2}^{\infty } \text{If}\left[\text{PrimeQ}[p],\frac{p^2+1}{p^2-1},1\right]
$$
in Mathematica 12.0, it gives out the value $1$.
The result is ridiculous, for that according to ...
- 225
0
votes
1
answer
91
views
Return last value of While function
I want to make a function that performs a multiplication with Inner i number of times using a ...
2
votes
1
answer
72
views
Set default product
I want to set a default product in Mathematica in place of the standard product. Specifically, I want to change the standard product for CenterDot so that when I ...
1
vote
3
answers
84
views
Summation and product term expressed in Mathematica [duplicate]
I have the following term which I would like to express correctly in Mathematica:
$$\sum_{i=1}^{m}\frac{1}{\prod_{j=1,j\neq i}^m(\rho_i-\rho_j)}$$
This means that for $m=3$ for example you should ...
- 181
5
votes
2
answers
161
views
How to write down a product with omitted terms?
I have the following term which I would like to express correctly in Mathematica:
$$
\prod_{j=1,j\neq i}^m(\rho_i-\rho_j)
$$
Can you please help?
- 181
3
votes
1
answer
518
views
Outer (dyadic) product between vectors of the same index in two lists
I have two lists of vectors and I want to take the outer product between elements in the lists of the same index. Using either Outer or TensorProduct works for e.g. the first two indices:
...
- 31
1
vote
2
answers
91
views
Where is the "mistake in the recursion" while there is no recursion? [closed]
So my code is as follows
xi = Exp[2*Pi I/13]
tauA = xi + xi^(-1)
sigma[tau_, n_] := tau^n
Product[(x - sigma[tauA, i]), {i, 3, 8}] // FullSimplify
This should ...
- 115
3
votes
1
answer
211
views
How to create a dot product version of the product function
I would like to create a function to matrix multiply (dot product) n matrices together, where n is large, for example
M1*M2*M3*M4*M5*...*Mn
I know there is the 'product' function that can do this ...
user63517
2
votes
1
answer
41
views
How to PowerExpand a generic Product?
I have:
PowerExpand[Log[Product[f[i], {i, 1, n}]]] // InputForm
(* Output: Log[Product[f[i], {i, 1, n}]] *)
However, I would expect to get the following as the ...
- 757
3
votes
4
answers
493
views
Dot product result has wrong dimension [closed]
I'm doing a small project and I've encountered a problem while using Mathematica. I should mention that I'm kinda new to this software, so maybe it's just something I haven't grasped yet.
Anyway, I ...
- 35
4
votes
2
answers
191
views
Why does this simple ratio of products not simplify?
Why does this ratio of products not Simplify to a[n]?
Clear[a,k,n]
$Assumptions={n>1}
Simplify[ Product[a[k], {k, 1, n}] / Product[a[k], {k, 1, n - 1}] ]
...
- 847
2
votes
2
answers
239
views
Sums of products with $ n $ variables
I want to be able to compute a function of $ n $ indices which looks as follows
if $ n>2 $:
$$
\sum_{(i=1,j=1,k=1,l=1,...), (i\neq j\neq k \neq l \neq ...)}^{n} x_{i}x_{j}(x_{k}^2+y_{k}^2)(x_{l}^...
- 23
1
vote
2
answers
310
views
Calculating the series expansion of a theta function
I have defined the q-theta function as follows:
$$\theta(x;q) = \prod_{k=0}^{\infty} (1-q^k x)(1-q^{k+1}/x)$$
I want to calculating, using this, the series expansion of the following series:
$$\...
- 203