maxima - 阻止最大值询问正、负或零

Question

有没有办法告诉 maxima 一个表达式总是积极的？这是一个示例片段，它导致 maxima 对表达式 sin(a)*x 提出问题:

声明([a,x,y],real);
ca: cos(a) = (x/(sqrt(x*x + y*y)));
a1:解决(ca，a)[1]；
解决(a1，y)；

Answer 1

您可以使用 assume .来自千里马自己的文档:

    -- Function: assume (, ..., )     Adds predicates , ...,  to the current context.     If a predicate is inconsistent or redundant with the predicates in     the current context, it is not added to the context.  The context     accumulates predicates from each call to `assume'.     `assume' returns a list whose elements are the predicates added to     the context or the atoms `redundant' or `inconsistent' where     applicable.     The predicates , ...,  can only be expressions     with the relational operators `=' and `>'.     Predicates cannot be literal equality `=' or literal inequality     `#' expressions, nor can they be predicate functions such as     `integerp'.     Compound predicates of the form ` and ... and '     are recognized, but not ` or ... or '.  `not     ' is recognized if  is a relational predicate.     Expressions of the form `not ( and )' and `not     ( or )' are not recognized.     Maxima's deduction mechanism is not very strong; there are many     obvious consequences which cannot be determined by `is'.  This is     a known weakness.     `assume' evaluates its arguments.     See also `is', `facts', `forget', `context', and `declare'.

 Examples:

      (%i1) assume (xx > 0, yy < -1, zz >= 0);
      (%o1)              [xx > 0, yy < - 1, zz >= 0]
      (%i2) assume (aa < bb and bb < cc);
      (%o2)                  [bb > aa, cc > bb]
      (%i3) facts ();
      (%o3)     [xx > 0, - 1 > yy, zz >= 0, bb > aa, cc > bb]
      (%i4) is (xx > yy);
      (%o4)                         true
      (%i5) is (yy < -yy);
      (%o5)                         true
      (%i6) is (sinh (bb - aa) > 0);
      (%o6)                         true
      (%i7) forget (bb > aa);
      (%o7)                       [bb > aa]
      (%i8) prederror : false;
      (%o8)                         false
      (%i9) is (sinh (bb - aa) > 0);
      (%o9)                        unknown
      (%i10) is (bb^2 < cc^2);
      (%o10)                       unknown