The ''Kuṭṭākāra Śirōmaṇi'' is a medieval Indian treatise in

Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...

devoted exclusively to the study of the Kuṭṭākāra, or

Kuṭṭaka Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ''ax'' + ''by'' = ''c'' where ''x'' and ''y'' are unknown quantities and ''a'', ''b'', and ''c'' ar ...

, an

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

for solving

linear Diophantine equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknown (mathematics), unknowns with integer coefficients, such that the only equation solving, solutions of interest are the integer ones. A l ...

s. It is authored by one Dēvarāja about whom little is known. From statements given by the author at the end of the book, one can infer that the name of Dēvarāja's father was Varadarājācārya, then famously known as Siddhāntavallabha. Since the book contains a few verses from the Lilavati, it should have been composed during a period after the Lilavati was composed, that is after 1150 CE. Treatises such as the Kuṭṭākāra Śirōmaṇi devoted exclusively to specialized topics are very rare in Indian mathematical literature. The algorithm was first formulated by

Aryabhata I Aryabhata (ISO 15919, ISO: ) or Aryabhata I (476–550 Common Era, CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta era, Gupta Era and produced works su ...

and given in verses in the Ganitapada of his

Aryabhatiya ''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Sanskrit astronomical treatise, is the ''magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that th ...

. Aryabhata's description of the algorithm was brief and hence obscure and incomprehensible. However, from the interpretations of the verses by later

Indian mathematicians chronology of Indian mathematicians spans from the Indus Valley civilisation and the Vedas to Modern India. Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians ...

we now have a fairly clear understanding of the original formulation of the algorithm. The Kuṭṭākāra Śirōmaṇi is one of the most comprehensive treatment of the algorithm. Devraja also wrote a self commentary, the Maha Laksami Muktavali on the Kuttakara Siromani to further explain the method. The Kuṭṭākāra Śirōmaṇi is divided into three chapters, or ''Paricchedas''. The first chapter of the book is on the Sāgra Kuṭṭākāra, the second chapter deals with the Niragra Kuṭṭākāra. This chapter also contains descriptions of the Samśliṣṭa Kuṭṭākāra. The third and the last chapter is on the Miśra-Śreṇi-Miśra-Kuṭṭākāra. The book also discusses the Vallikakuṭṭākāra and Sthitakuṭṭākāra. The methods are explained in detail with the help of illustrations and their important applications in Astronomy.

References

Indian mathematics {{math-hist-stub

See also

References