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     _D_E_P_A_R_T_M_E_N_T _O_F _C_O_M_P_U_T_E_R _S_C_I_E_N_C_E
     _U_N_I_V_E_R_S_I_T_Y _O_F _W_A_T_E_R_L_O_O
     _S_E_M_I_N_A_R _A_C_T_I_V_I_T_I_E_S

     _S_Y_M_B_O_L_I_C _C_O_M_P_U_T_A_T_I_O_N _S_E_M_I_N_A_R
                                - Tuesday, July 19, 1983.

     Prof. J.H. Davenport of Emmanuel College will speak  on
     ``Integration of Algebraic Functions''.

     TIME:                3.30 PM

     ROOM:              MC 5158

     ABSTRACT

     The   integration   of   algebraic   functions    (e.g.
     sqrt(x**2-1))  is  a  more complicated problem than the
     integration of rational  or  transcendental  functions.
     It  requires the use of several concepts from algebraic
     geometry, as well  the  application  of  many  familiar
     techniques  of  computer  algebra  in new contexts.  We
     will discuss ``Coates' algorithm'', the key to our  ap-
     proach  to  integration,  and  show how it ``almost al-
     ways'' enables one to find  closed  form  integrals  or
     prove  that they do not exist.  We will then sketch the
     filling of the ``almost always'' gap, and mention  some
     extensions.  The talk should be largely intelligible to
     those without an algebraic geometry background.

                       July 12, 1983