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Table of Contents - 10.9.4. Univariate polynomials

According to Wikipedia ("Polynomial", 23-Dec-2019, https://en.wikipedia.org/wiki/Polynomial) "A polynomial in one indeterminate is called a univariate polynomial, a polynomial in more than one indeterminate is called a multivariate polynomial." In this sense univariate polynomials are defined as multivariate polynomials restricted to one indeterminate/polynomial variable in the following, see ply1bascl2.

According to the definition in Wikipedia "a polynomial can either be zero or can be written as the sum of a finite number of nonzero terms. Each term consists of the product of a number - called the coefficient of the term - and a finite number of indeterminates, raised to nonnegative integer powers.". By this, a term of a univariate polynomial (often also called "polynomial term") is the product of a coefficient (usually a member of the underlying ring) and the variable, raised to a nonnegative integer power.

A (univariate) polynomial which has only one term is called (univariate) monomial- therefore, the notions "term" and "monomial" are often used synonymously, see also the definition in [Lang] p. 102. Sometimes, however, a monomial is defined as power product, "a product of powers of variables with nonnegative integer exponents", see Wikipedia ("Monomial", 23-Dec-2019, https://en.wikipedia.org/wiki/Mononomial). In [Lang] p. 101, such terms are called "primitive monomials". To avoid any ambiguity, the notion "primitive monomial" is used for such power products ("x^i") in the following, whereas the synonym for "term" ("ai x^i") will be "scaled monomial".

  1. cps1
  2. cv1
  3. cpl1
  4. cco1
  5. ctp1
  6. df-psr1
  7. df-vr1
  8. df-ply1
  9. df-coe1
  10. df-toply1
  11. psr1baslem
  12. psr1val
  13. psr1crng
  14. psr1assa
  15. psr1tos
  16. psr1bas2
  17. psr1bas
  18. vr1val
  19. vr1cl2
  20. ply1val
  21. ply1bas
  22. ply1lss
  23. ply1subrg
  24. ply1crng
  25. ply1assa
  26. psr1bascl
  27. psr1basf
  28. ply1basf
  29. ply1bascl
  30. ply1bascl2
  31. coe1fval
  32. coe1fv
  33. fvcoe1
  34. coe1fval3
  35. coe1f2
  36. coe1fval2
  37. coe1f
  38. coe1fvalcl
  39. coe1sfi
  40. coe1fsupp
  41. mptcoe1fsupp
  42. coe1ae0
  43. vr1cl
  44. opsr0
  45. opsr1
  46. mplplusg
  47. mplmulr
  48. psr1plusg
  49. psr1vsca
  50. psr1mulr
  51. ply1plusg
  52. ply1vsca
  53. ply1mulr
  54. ressply1bas2
  55. ressply1bas
  56. ressply1add
  57. ressply1mul
  58. ressply1vsca
  59. subrgply1
  60. gsumply1subr
  61. psrbaspropd
  62. psrplusgpropd
  63. mplbaspropd
  64. psropprmul
  65. ply1opprmul
  66. 00ply1bas
  67. ply1basfvi
  68. ply1plusgfvi
  69. ply1baspropd
  70. ply1plusgpropd
  71. opsrring
  72. opsrlmod
  73. psr1ring
  74. ply1ring
  75. psr1lmod
  76. psr1sca
  77. psr1sca2
  78. ply1lmod
  79. ply1sca
  80. ply1sca2
  81. ply1mpl0
  82. ply10s0
  83. ply1mpl1
  84. ply1ascl
  85. subrg1ascl
  86. subrg1asclcl
  87. subrgvr1
  88. subrgvr1cl
  89. coe1z
  90. coe1add
  91. coe1addfv
  92. coe1subfv
  93. coe1mul2lem1
  94. coe1mul2lem2
  95. coe1mul2
  96. coe1mul
  97. ply1moncl
  98. ply1tmcl
  99. coe1tm
  100. coe1tmfv1
  101. coe1tmfv2
  102. coe1tmmul2
  103. coe1tmmul
  104. coe1tmmul2fv
  105. coe1pwmul
  106. coe1pwmulfv
  107. ply1scltm
  108. coe1sclmul
  109. coe1sclmulfv
  110. coe1sclmul2
  111. ply1sclf
  112. ply1sclcl
  113. coe1scl
  114. ply1sclid
  115. ply1sclf1
  116. ply1scl0
  117. ply1scln0
  118. ply1scl1
  119. ply1idvr1
  120. cply1mul
  121. ply1coefsupp
  122. ply1coe
  123. eqcoe1ply1eq
  124. ply1coe1eq
  125. cply1coe0
  126. cply1coe0bi
  127. coe1fzgsumdlem
  128. coe1fzgsumd
  129. gsumsmonply1
  130. gsummoncoe1
  131. gsumply1eq
  132. lply1binom
  133. lply1binomsc