. . . AND . . .

>>> A set of three new Maple functions

The Maple V Share Library is a wonderful facility for mathematicians comprising some 140 Maple routines, packages and worksheets written by Maple users and contributed freely to the Maple community. It used to be bundled as part of the Maple package but that practice ceased with Maple 6. Only some 25% of this vast corpus of knowledge is currently available via the Maplesoft Application Center. The remaining 75% was effectively "lost" to mathematicians—until now!

John Maplenut has written a short program which allows the Maple V Share Library for Windows to be accessed directly from all versions of Maple up to and including version 11. The program apparently also works with Mac versions but John has had no direct experience of other Maple platforms.

John has also been through the original Maple V Share Library from beginning to end and debugged programs which performed badly, or not at all. This enormous task took in excess of three years to complete!

Maple versions 5 to 8 give the best results, later versions have problems with a few packages. For instance, the programs "shoot" and "macroC" will not work with versions above Maple 8. Please advise of programs which do not work properly in your Maple version.

You can download the fruits of all this labour from this website. John's latest "shareman" program and the latest debugged Maple V share library are contained within a compressed folder of 3.4 Mb named sharelib.zip. Unzip in the usual way and follow the simple installation details within the text file which emerges.

Please note that sharelib.zip is available via the Maplesoft Application Center (Maple Tools/Shared Libraries) but it may not always be the latest version. It is in the top 5% of the 'Most-Downloaded' and 'Top-Rated' applicaions.

John wishes to be informed of any bugs which may have escaped his attention. He can be contacted via maplenut@tiscali.co.uk 

= = = = = = = = = = = = = = = = = = = = =

A set of three new Maple functions is also offered for download for the first time by John Maplenut.

IntRange:

IntRange can split 'Int' type functions into different areas, and combine different functions with different ranges, to produce a single definite integral. Specifically:

• Given an integral and a range, IntRange returns a new integral and range.
• Given a list of integrals and a range, IntRange returns a combined integral with the given range.
• Given an integral and a list of points that can include one or both endpoints, IntRange returns a single definite integral containing the sum of positive and negative values.
• If an empty list of points [ ] exists, IntRange uses the zeros program below to create a list of points.

zeros: functions and polynomials

The function zeros(f(x), x = a .. b) returns all the points where f(x) is zero in the interval [a, b] as a list of real values. You will need to increase digits by 2 or more if values are missing.

hermite: interpolation

The function hermite uses hermite interpolation and computes the polynomial of degree less than or equal to 2n-1 in the variable x that interpolates the list of values:
[x[1],x[2],...x[n]], [y[1],y[2],...y[n]], [dy/dx[1],dy/dx[2],...dy/dx[n]].

All the independent values must be distinct otherwise an error occurs.

You can download this set of Maple routines from a compressed folder named maplenuts.zip. Unzip in the usual way and follow the simple installation details within the text file which emerges.

This site was last updated 10 May 2008

= = = = = = = = = = = = = = = = = = = = = = = =

"He ain't heavy, he's my brother"

My name is Peter and I administer this basic website on behalf of my brother. John realises his work could be of use to other mathematicians but he labours under a particular bête noire which prevents him from actively pursuing social contact with others.

John has a very interesting condition called Asperger's Syndrome [also known as High-Functioning Autism or Pervasive Developmental Disorder], which renders him socially incapacitated in some important respects, but comes with a degree of single-mindedness you or I cannot begin to comprehend. He was labelled AS at the age of 67—does this make him one of the oldest persons ever to be diagnosed with the condition?

It is reckoned a sizeable number of prominent scientists down the ages had AS [Albert Einstein and Isaac Newton for instance]. Some of the monumental advances in science and mathematics may only have been possible because these AS individuals were able to cast aside 'normal' constraints relating to time, social responsibility and physical well-being. Society has benefited from these individuals, but at a heavy personal price.

My brother was born in 1934, ten years before the condition was first described by the Austrian paediatrician Hans Asperger. John's childhood spanned the Second World War and was exceedingly troubled. He was a loner bearing the burden of a condition which had yet to be delineated.

John is a gifted self-taught programmer and mathematician. Sadly, he never had the opportunity to go beyond secondary education. But to be frank, his AS would probably have prevented him benefiting from a formally-structured university course.

John joined the Royal Air Force during the Cold War in the 1950s. For much of his service he was a fighter plotter in the British Sector in Germany, close to the Russian border. This occupation was ideally suited to his AS characteristics. He very much enjoyed the work, which required great attention to detail.

He was demobbed in 1957 and shortly afterwards emigrated to Australia under the assisted-passage scheme then in operation in the UK. He drifted apart from his family back home in England and was effectively lost to us for many years. He held down a number of mundane jobs which allowed him the freedom to pursue the only real loves of his life—computer programming and pure mathematics.

John is actually my half-brother, although this fact has no relevance to our relationship. The mother we share conceived him whilst in lodgings after breaking with her first husband. In the final years of her life mother was haunted by the 'loss' of her firstborn. I finally managed to track down John through an article in the Australian press. He could manage only a two-page letter to make up for the missing years; but at least mother died knowing he was alive and well. It is so sad she did not live long enough to learn of the condition which led to his waywardness as a child. I am sure she blamed herself for much of the way he had turned out.

With advancing age John became very vulnerable. He was living alone in a flat in a Queensland suburb, shunning outside support and rapidly losing mobility. His plight was exacerbated by binge drinking, heavy smoking and an involuntary addiction to Diazepam, a drug which had foolishly been prescribed to treat what others had perceived as "depression" and sleep disorders. He also had several other medical problems to contend with. 

From our sporadic telephone conversations it was clear he was dreading the advancing years. He was never one to make friends, although others sought his company. Over the years his acquaintances had dwindled and he was effectively alone in the world.

In the summer of 2000 I flew out to Australia to properly appraise his situation and to work out some sort of strategy for the future. It was 34 years since we had last met.

I found John in decline. He would soon lose his independence and it was inconceivable that he could settle in a residential home with his particular problems and idiosyncrasies. On my return to the UK I bought a little house some 30 miles from my matrimonial home. As it turned out the stock market nose-dived shortly afterwards. Rescuing John preserved, even enhanced, most of my hard-won assets.

When I brought John back to England—a minor logistical miracle in itself and unimaginably stressful for John, who was forced to travel alone—I had no idea he was suffering from AS. I had remembered him from my childhood years as a 'difficult' person, but I put that down to the eight-year age gap between us. He was somebody I looked up to from a distance which he himself had imposed. There had been little contact between us in the intervening years.

Incidentally, when I collected him from Gatwick airport he had one suitcase and just a few hundred pounds—not much to show for 34 years "down under."

A bilateral ear infection of five years duration was cleared up in less than a week with the right treatment. He was effectively weaned off tranquilisers within a month. Access to alcohol is now severely restricted but he is allowed cigarettes ad libitum, as long as he rolls his own! He gets through about 8 kgs of tobacco every year—I travel over to Belgium to procure supplies or he would bankrupt us both.

Shortly after his return a visiting friend took me to one side and suggested John was suffering from AS. Like so many other people I was ignorant of the condition. I managed to get a referral to a psychiatrist specialising in AS and other autistic spectrum disorders. She was convinced he had all the characteristics of the condition and the diagnosis was made.

Because his condition is well cloaked, except to a persistent enquirer, John had previously been labeled by a succession of so-called experts, mostly psychiatrists, as suffering from depression, obsessive-compulsive disorder, early dementia and even schizophrenia. John has never suffered from any of these conditions. 

Initially, John could not see the point of pursuing a diagnosis of AS at his time of life. But almost imperceptibly this new knowledge has brought him peace of mind. Everything now falls into place and he appears quite proud to be known as an AS sufferer!  Now that he is properly understood, and his future is assured, he has emerged as a happy and contented soul. He has a wicked, if unsophisticated, sense of humour. He is in his early 70s, but going on 17.

John will be mortified when he finds out his life has been laid bare in this fashion—hence the need for anonymity. On this occasion I will ignore his entreaties. I believe it is important the plight of older people with AS, many undiagnosed, is given more prominence. These people receive little or no attention and are particularly vulnerable in later life. So many mature AS sufferers lead lives of untold misery because of ignorance, prejudice and misunderstanding.

John tells me he was obliged by family circumstances to look after me and my twin brother when we were toddlers. He understandably resented this responsibility at such an early age. The roles are now reversed and I look after him. At times he is a burden, but I can bear that. Sufficient reward is the sprouting of brotherly ties which were never present the first time around. Both our lives have been enriched by this re-association.