Note that MuPAD is the only non-commercial system in this test. An alpha release of MuPAD for Windows exists but is not complete and therefore not available for external users. We hope to publish it in Summer 1996. -- This c't testsuite paper is based on the MuPAD release 1.2.2.
For the current test results of MuPAD, please refer to the Wester's testsuite paper compiled by Paul Zimmermann. It will be updated periodically with new features available in the MuPAD development version.
1
---------------------- + 3
1
------------------ + 7
1
------------- + 15
1
--------- + 1
1
--- + 292
...
Here "..." represents a real between one and infinity. Thus for example the continued fraction of 0 is 1/..., that of an integer n is (n+1)/....
1
------------------- + 2
1
--------------- + 4
1
----------- + 4
1
------- + 4
1
--- + 4
...
A continued fraction in MuPAD is an element of the domain CF which provides some further methods. At first we want to compute an intervall that contains the continued fraction for PI that was computed above.
103993/33102, 104348/33215
Now we get a continued fraction for the golden-ratio (1+sqrt(5))/2 from that of sqrt(5) via the fractional linear form L(x)=(x+1)/2.
1
----------------------------------------------- + 1
1
------------------------------------------- + 1
1
--------------------------------------- + 1
1
----------------------------------- + 1
1
------------------------------- + 1
1
--------------------------- + 1
1
----------------------- + 1
1
------------------- + 1
1
--------------- + 1
1
----------- + 1
1
------- + 1
1
--- + 1
...
Finally we want to show how to perform arithmetic on continued fractions. At first we compute the continued fraction for PI+sqrt(5).
1
----------------------- + 5
1
------------------- + 2
1
--------------- + 1
1
----------- + 1
1
------- + 1
1
--- + 5
...
The continued fraction for PI*sqrt(5).
1
------------ + 7
1
------- + 40
1
--- + 3
...
The continued fraction for PI^2/sqrt(5).
------------------- + 4
1
--------------- + 2
1
----------- + 2
1
------- + 2
1
--- + 2
...