Questions tagged [arithmetic]
Questions on arithmetic operations in Mathematica.
93
questions
118
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1
answer
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Why are numeric division and subtraction not handled better in Mathematica?
There is something that has been troubling me for a while. At least through version 10.0 the performance of a / b and a - b is ...
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42
votes
2
answers
1k
views
Is there a difference between Divide[a,b] and a/b?
In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ...
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36
votes
8
answers
3k
views
Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$
Insert $+$, $-$, $\times$, $/$, $($, $)$ into $123456789$ to make it equal to $100$.
Looks like a question for pupils, right?
In fact, if the available math symbols are limited to addition ($+$), ...
- 62.9k
29
votes
2
answers
681
views
Should 0 * 5ft be 0 or 0ft?
After playing with the new quantity system in Mathematica 9 for a while, I keep stumbling over this issue:
0 * Quantity[1, "Meters"]
is not the same as
...
- 35.9k
18
votes
6
answers
5k
views
Puzzle with Mathematica
Hello everyone,
This is a puzzle I got from someone via social media. Basically, we need to fill up the boxes with the numbers 1-9 (no repetitions) that fit the multiplication and addition operations.
...
- 347
17
votes
1
answer
1k
views
How to prevent reduction of a fraction into lowest terms?
I have a question about the concept of simplification. I want to explain it with an example.
When I write the fraction $4/8$ in Mathematica, the output is
1/2.
How ...
- 739
16
votes
8
answers
3k
views
Product of elements of a list
Sum is for functions; Total is for a list. Product is for a function; what is the command ...
user21376
16
votes
3
answers
1k
views
How to enter a repeating decimal in Mathematica
I don't understand how to manipulate numbers with repeating decimal in Wolfram Mathematica language.
For example 0.3... does not work as input and I don't see how ...
- 3,003
16
votes
1
answer
329
views
How does Plus work on machine precision Real arguments?
I thought Kahan's summation method would make a nice example for students to use to think about round-off error
[W. Kahan,
Pracniques: Further Remarks on Reducing Truncation Errors,
Commun. ACM 8 (...
- 233k
15
votes
3
answers
11k
views
Expressing a decimal as a fraction in lowest terms
How can I express a decimal such as 0.1845095405274387 as a fraction in its lowest terms?
- 359
13
votes
2
answers
235
views
Arithmetic operations on NumericArrays
Currently, NumericArrays are directly supported by the most important array-related functions, what makes them a very attractive data structure for implementing ...
- 61.3k
11
votes
1
answer
173
views
Trace of -{1} expression
I'm trying to understand Trace. Usually it doesn't repeat but it adds {-1,-1} for his simple expression after having a correct ...
- 619
9
votes
2
answers
856
views
Why am I seeing what looks like a violation of operator precedence?
Why is it that when I evaluate
2*2.848529281693615`+3*-0.5155083247776808`
I get
(* -2.93688 *)
which is wrong.
...
- 2,517
9
votes
1
answer
232
views
Arbitrary-Precision Arithmetic behaves unexpectedly
I want to understand how small numerical errors propagate through a computation and may drastically change the final result.
To this end, I consider a toy world in which every number is limited to ...
- 389
8
votes
4
answers
1k
views
How to recover Pauli matrices properties in Mathematica?
I want to do a cross or dot product involving a vector of Pauli matrices
$ \vec\sigma=(\sigma^1, \sigma^2, \sigma^3) $; for example, $ \vec\sigma\times\vec\sigma=2\mathrm i\vec\sigma $ and $ \vec\...
- 81
8
votes
3
answers
388
views
Improving Map Function on Lists
Dealing with spectral data (2D lists) where offsets (corresponding 1D list) must be removed from each individual spectrum. Looking for feedback on improvements over my current method.
...
- 560
8
votes
4
answers
1k
views
Countdown arithmetic solver
In the numbers game in countdown, contestants are given 6 numbers with which they must reach a seventh number with basic arithmetic. The only operations allowed are addition, subtraction, ...
- 8,547
7
votes
2
answers
2k
views
How to do binary calculation？
For example, $a=0.10101$ in binary representation.
Then how to calculate $a^2$ directly in mathematica?
Is there any function turning binary into decimal? I only found its inverse...
- 172
7
votes
2
answers
237
views
Is there a way to show the details of a numerical computation?
I have recently started using Mathematica as a calculator while teaching (definitely overkill, but I try to use as few tools as possible). I would like my students to be able to trace simple numerical ...
- 4,312
7
votes
1
answer
177
views
Running Mathematica in 'SpouseMode'
In this previous question I looked into a deprecated capability of Mathematica from Version 2.
Mathematica command that allows it to read my intentions
Thanks to all for your answers. I note that ...
- 7,113
5
votes
14
answers
2k
views
Sum of Squares without multiplication
I want to sum the squares for a given number N from 1 without using Multiplication. Is it possible?
- 75
5
votes
3
answers
533
views
How to find a longest word path in dictionary?
Cross post here
A word path means the last character of the last word is same to the first character of the next word.And the path have no duplicated word.If I have $55$ words,I can find it with this ...
- 26.1k
5
votes
1
answer
246
views
Does Mathematica simplify calculation when encounter zero?
e.g.
when Mathematica Calculating f[x0]=A[x0] B[x0],
where A[x] & B[x] could be some complicated high dimensional function.
Will Mathematica outcome 0 directly ...
5
votes
1
answer
414
views
Why can't I remove Orderless from Plus?
I am making some random algebra equations, and I want to have the ordering be random too, such that if my random equation generator makes x+1, the output stays <...
- 4,642
4
votes
3
answers
2k
views
Permanently rounding numbers/values to a given number of significant figures
I am searching for a simple way of rounding and setting an input to a desired number of significant figures. There are a vast number of posts that discuss similar problems, but none address this issue....
4
votes
2
answers
379
views
Interchanging addition and multiplication
Suppose I have an expression that employs addition and multiplication, but no subtraction or division:
$$
2 a + 5 b x^3 + c \;.
$$
I would like to change this to
$$
(2 + a) (5 +b + x +x +x) c \;,
$$
...
- 4,649
4
votes
2
answers
200
views
Multiplication non-deterministic?
I have two vectors of 134 elements each ($mu$, and $gt$). $mu$ contains Integers, and $gt$ contains machine precision Reals. I execute the following simple expression multiple times without changing ...
- 175
4
votes
1
answer
401
views
multiply two vectors, component by component [closed]
Would like to take two vectors and multiply components at the same index.For example {a1, a2, a3} x {b1, b2, b3} to produce {a1 b1, a2 b2, a3 b3}.
The following works, but are there some alternatives?...
- 1,027
4
votes
2
answers
2k
views
Floating point addition not associative
Can anybody explain the following behavior?
x = 0.2 + (0.3 + 0.1);
y = (0.2 + 0.3) + 0.1;
x == y (* -> True *)
But actually the variables do not exactly ...
- 637
4
votes
1
answer
87
views
Simplify expressions with modulo 2 (Boolean algebra)
Suppose I have a (Boolean algebra) expression
a = p1 x^2 + p2 x (x-1) + 3 p3 + 4 p4 x
where p1, ..., ...
- 179
4
votes
2
answers
110
views
Raise a table of pre-existing data to the power of of one of the variables
NOTE: I have edited this question to give a table whose first elements don't count up from 0 to 5.
I'm using a sample table ...
- 2,121
4
votes
3
answers
193
views
A sudoku-like collection puzzle
I have a puzzle. I'm given a collection of $n$ lists, all of equal (but arbitrary) length $l$. These lists are made up of 0s and a few filled in numbers, like so:
{ {0, 2}, {0,0}, {6, 0}, {0,0} }
...
- 3,604
4
votes
1
answer
148
views
Machine Epsilon is not equal to $MachineEpsilon [duplicate]
I try to wrap my head around machine precision calculations in Mathematica (11.2, Linux). I do not understand the following behavior:
...
- 43
4
votes
0
answers
80
views
Force computation on IEEE float/double
I'm checking two different procedures that will eventually be used with regular floating point arithmetic. I need to estimate numerical error arising from floating point arithmetic.
Is there a way to ...
- 211
4
votes
0
answers
170
views
How can one best implement the multiplication of octonions using the Quaternions package?
I excerpt from p. 4 of the recent paper of P. J. Forrester (https://arxiv.org/pdf/1610.08081.pdf):
"Let $p_1$ and $p_2$ be quaternions. The octonion algebra consists of elements of the form $p_1+p_2 ...
- 2,315
4
votes
0
answers
121
views
Simple arithmetic with Irrationals fails [closed]
While solving a simple puzzle that asked for a few calculations in plane geometry, I ended up with this expression:
$-\frac{55}{2}+\frac{\sqrt{27233}}{2}+\frac{1}{2}(55-\sqrt{27233})$
Or, in ...
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3
votes
3
answers
149
views
Why does the Mathematica give different numerical results?
Why do the two inputs give different values?
in:=(-y)^a /. a -> 2.99 /. y -> -2
out:=7.94474
and
...
- 91
3
votes
2
answers
3k
views
Doing arithmetic with binary numbers
How do I execute binary operations in Mathematica? I want to to multiply say 1010101011 (binary) to 1111101110 (binary) and getting the result 10100111101111111010? Then I want to add the result to ...
- 351
3
votes
2
answers
252
views
Applying Mod on list of list with outcomes +1, -1, other
I have a list
lis = {{7, 8}, {17, 9}, {11, 10}, {12,10}}
I want to apply Mod to each pair with output +1,-1 or ...
- 2,304
3
votes
1
answer
111
views
Why Divide does not give the same answer? [closed]
I saw a question on Facebook $8\div2 (2 + 2)=?$
Consider these inputs.
Divide[8, 2 (2 + 2)]
1
$8\div2 (2 + 2)$ using esc+div+esc
16
Why the results are ...
- 10.4k
3
votes
1
answer
161
views
Solving calculation puzzle [closed]
I recently got asked how to achieve a result of 100 only using the numbers {1,7,7,7,7} (the number 1 can be used only once and ...
- 1,134
3
votes
1
answer
200
views
How can I redefine multiplication?
For instance, I want 0 Infinity = 0
I tried this: Unprotect[Times];Times[Infinity,0]=0;Times[0,Infinity]=0;Protect[Times];
But ...
- 3,473
3
votes
2
answers
117
views
Can I make RandomInstance use exact arithmetic?
When using RandomInstance on a GeometricScene the answer loses precision when root objects are encountered. Is there a way to ...
- 9,043
3
votes
2
answers
81
views
Advice for making addition and multiplication tables for my kid
I'm working with my 6 year old on understanding and mastering addition. As a result, I want to be able to make some custom addition (and eventually multiplication) tables for her to fill out.
...
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3
votes
1
answer
183
views
Generating prime factorizations from an integer's digits by inserting * and ^ into the digit sequence
Problem
Given a positive integer, output all possible valid prime-factorization "statements" thereof created by inserting zero or more multiplication (*) symbols and zero or more power (^) symbols ...
- 199
3
votes
1
answer
124
views
Forcing divisions to be a machine-precision floating point divisions instead of multiplication by inverse
I want to imitate machine-precision, de facto IEEE division on Mathematica. On my quick trials I find this surprisingly hard to accomplish, since Mma rewrites a / b ...
- 18.6k
3
votes
0
answers
73
views
Problem with Mathematica Relationship Building
When I enter the following to get Mathematica to open my pod door I get
Could someone try and replicate this? Also, my name is not Dave and I throw my own error...
...
- 7,113
2
votes
6
answers
287
views
Is there any function that creates an array from 1 to n, repeating each value m times?
I am trying to implement SparseArray, using the function With to give the condition for different matrix elements. I would need ...
- 1,294
2
votes
3
answers
594
views
Rounding Real number
I have real numbers in array, I want to round (or truncate) these numbers to 2-digit after decimal point, then I want to write values to Excel File
For example if I have
...
- 73
2
votes
1
answer
371
views
Why is arithmetic faster for inexact arithmetic?
I have been trying to compute eigenvalues of a rather sizable matrix A, about $500 \times 500$ (but sparse). I asked Mathematica to compute ...
- 463