Symbolic Math Toolbox 5.3

Variable Precision Arithmetic

Demonstrate variable precision arithmetic with the Symbolic Math Toolbox™ product.

Compute 19/81 to 70 digits. Notice the repeated pattern of digits. "vpa" stands for variable precision arithmetic.

vpa 19/81 70

ans =

0.2345679012345679012345679012345679012345679012345679012345679012345679

Compute pi to 780 digits. Notice the string of 9's near the end.

vpa pi 780

ans =

3.14159265358979323846264338327950288419716939937510582097494459230781640628
6208998628034825342117067982148086513282306647093844609550582231725359408128
4811174502841027019385211055596446229489549303819644288109756659334461284756
4823378678316527120190914564856692346034861045432664821339360726024914127372
4587006606315588174881520920962829254091715364367892590360011330530548820466
5213841469519415116094330572703657595919530921861173819326117931051185480744
6237996274956735188575272489122793818301194912983367336244065664308602139494
6395224737190702179860943702770539217176293176752384674818467669405132000568
1271452635608277857713427577896091736371787214684409012249534301465495853710
5079227968925892354201995611212902196086403441815981362977477130996051870721
134999999837297804995

Compute exp(sqrt(163)*pi) to 30 digits.

vpa exp(sqrt(163)*pi) 30

ans =

262537412640768743.999999999999

The value might be an integer.

Compute the same value to 40 digits.

vpa exp(sqrt(163)*pi) 40

ans =

262537412640768743.9999999999992500725972

So, the value is close to, but not exactly equal to, an integer.

Compute 70 factorial with 200 digit arithmetic.

f = vpa('70!',200)

f =

1.19785716699698917960727837216890987364589381425464258575553628646280095827
8984531968*10^100

How many digits in 70!?

parts=sscanf(char(f),'%f*10^%d');
parts(2)+1

ans =

   101

Compute the eigenvalues of the fifth order magic square to 50 digits.

digits(50)
A = sym(magic(5))
e = eig(vpa(A))

A =

[ 17, 24,  1,  8, 15]
[ 23,  5,  7, 14, 16]
[  4,  6, 13, 20, 22]
[ 10, 12, 19, 21,  3]
[ 11, 18, 25,  2,  9]


e =

                                                  65.0
 21.27676547147379553062642669797423083613217355600061
 13.12628093070921880252564308594914382322273438650663
  -13.126280930709218802525643085949143823222734386507
  -21.276765471473795530626426697974230836132173556001