** Problem :**compute .

>> fact(50); 30414093201713378043612608166064768844377641568960512000000000000

** Problem :**compute the prime decomposition of .

>> ifactor(fact(50)); [1, 2, 47, 3, 22, 5, 12, 7, 8, 11, 4, 13, 3, 17, 2, 19, 2, 23, 2, 29, 1, 31, 1, 37, 1, 41, 1, 43, 1, 47, 1]

The function `ifactor(n)`

returns a list where , and .

** Problem :**compute .

>> _plus(1/i$i=2..10); 4861/2520

In MuPAD each arithmetic operator has a functional form, here `_plus`

for
addition, so for example `_plus(a,b)`

is the same as `a+b`

.

** Problem :**compute a numerical approximation of to **50** digits.

>> DIGITS:=50: float(exp(PI*sqrt(163))); 2.6253741264076874399999999999925007259719818568887e17

The floating-point numbers are output in scientific notation. This notation can be used as input too.

[New] ** Problem :**compute a numerical approximation of , where **J** is the
Bessel function of the first kind.

>> besselJ(2,1.0+I); 0.4157988694e-1 + 0.2473976415 I

Please note that floating-point numbers are ``contagious'': no `float`

instruction is needed here.

[New] ** Problem :**compute an infinite decimal representation of .

>> loadlib("numlib"): export(numlib): >> decimal(1/7); 0, [1, 4, 2, 8, 5, 7]

This result means that the decimal expansion of is .
Here the instruction `loadlib("numlib")`

loads the package.
Then `export(numlib)`

exports the functions of this package, i.e.
enables one to call them with a short name (otherwise we should write
`numlib::decimal`

).

[New] ** Problem :**compute the first terms of the continued fraction of .

>> contfrac(PI,5); 1 ---------------------- + 3 1 ------------------ + 7 1 ------------- + 15 1 --------- + 1 1 --- + 292 ...

The second (optional) argument of `contfrac`

specifies the
number of digits to be taken into account before computing the continued
fraction.

[New] ** Problem :**simplify .

>> radsimp(sqrt(2*sqrt(3)+4)); 1/2 3 + 1

[New] ** Problem :**simplify .

>> radsimp(sqrt(14 + 3*sqrt(3 + 2*sqrt(5 - 12*sqrt(3 - 2*sqrt(2)))))); 1/2 2 + 3

[New] ** Problem :**simplify .

>> 2*infinity-3; infinity

The symbol `infinity`

is implemented as a domain in MuPAD. This allows the
overloading of the basic arithmetic operations, together with the comparisons.
For example we can write in a MuPAD program `if a<infinity then ... end_if`

.

Sun Apr 23 10:32:10 MDT 1995