@@ -1,71 +1,71 @@
-
-           SOFIA LAPLACE AND INVERSE LAPLACE TRANSFORM PACKAGE
-
-                   C. Kazasov, M. Spiridonova, V. Tomov
-
-
-Reference:  Christomir Kazasov, Laplace Transformations in REDUCE 3, Proc.
-            Eurocal '87, Lecture Notes in Comp. Sci., Springer-Verlag
-            (1987) 132-133.
-
-Some hints on how to use to use this package:
-
-Syntax:
-
- LAPLACE(<exp>,<var-s>,<var-t>)
-
- INVLAP(<exp>,<var-s>,<var-t>)
-
-where <exp> is the expression to be transformed, <var-s> is the source
-variable (in most cases <exp> depends explicitly of this variable) and
-<var-t> is the target variable. If <var-t> is omitted, the package uses
-an internal variable lp!& or il!&, respectively.
-
-The following switches can be used to control the transformations:
-
-lmon:   If on, sin, cos, sinh and cosh are converted by LAPLACE into
-        exponentials,
-
-lhyp:   If on, expressions e**(~x) are converted by INVLAP into hyperbolic
-        functions sinh and cosh,
-
-ltrig:  If on, expressions e**(~x) are converted by INVLAP into
-        trigonometric functions sin and cos.
-
-The system can be extended by adding Laplace transformation rules for
-single functions by rules or rule sets.  In such a rule the source
-variable MUST be free, the target variable MUST be il!& for LAPLACE and
-lp!& for INVLAP and the third parameter should be omitted.  Also rules for
-transforming derivatives are entered in such a form.
-
-Examples:
-
-    let {laplace(log(~x),x) => -log(gam * il!&)/il!&,
-         invlap(log(gam * ~x)/x,x) => -log(lp!&)};
-
-  operator f;
-  let{
-    laplace(df(f(~x),x),x) => il!&*laplace(f(x),x) - sub(x=0,f(x)),
-
-    laplace(df(f(~x),x,~n),x) => il!&**n*laplace(f(x),x) -
-      for i:=n-1 step -1 until 0 sum
-        sub(x=0, df(f(x),x,n-1-i)) * il!&**i
-          when fixp n,
-
-    laplace(f(~x),x) = f(il!&)
-    };
-
-Remarks about some functions:
-
-The DELTA and GAMMA functions are known.
-
-ONE is the name of the unit step function.
-
-INTL is a parametrized integral function
-
-    intl(<expr>,<var>,0,<obj.var>)
-
-   which means "Integral of <expr> wrt <var> taken from 0 to <obj.var>",
-e.g. intl(2*y**2,y,0,x) which is formally a function in x.
-
-We recommend reading the file LAPLACE.TST for a further introduction.
+
+           SOFIA LAPLACE AND INVERSE LAPLACE TRANSFORM PACKAGE
+
+                   C. Kazasov, M. Spiridonova, V. Tomov
+
+
+Reference:  Christomir Kazasov, Laplace Transformations in REDUCE 3, Proc.
+            Eurocal '87, Lecture Notes in Comp. Sci., Springer-Verlag
+            (1987) 132-133.
+
+Some hints on how to use to use this package:
+
+Syntax:
+
+ LAPLACE(<exp>,<var-s>,<var-t>)
+
+ INVLAP(<exp>,<var-s>,<var-t>)
+
+where <exp> is the expression to be transformed, <var-s> is the source
+variable (in most cases <exp> depends explicitly of this variable) and
+<var-t> is the target variable. If <var-t> is omitted, the package uses
+an internal variable lp!& or il!&, respectively.
+
+The following switches can be used to control the transformations:
+
+lmon:   If on, sin, cos, sinh and cosh are converted by LAPLACE into
+        exponentials,
+
+lhyp:   If on, expressions e**(~x) are converted by INVLAP into hyperbolic
+        functions sinh and cosh,
+
+ltrig:  If on, expressions e**(~x) are converted by INVLAP into
+        trigonometric functions sin and cos.
+
+The system can be extended by adding Laplace transformation rules for
+single functions by rules or rule sets.  In such a rule the source
+variable MUST be free, the target variable MUST be il!& for LAPLACE and
+lp!& for INVLAP and the third parameter should be omitted.  Also rules for
+transforming derivatives are entered in such a form.
+
+Examples:
+
+    let {laplace(log(~x),x) => -log(gam * il!&)/il!&,
+         invlap(log(gam * ~x)/x,x) => -log(lp!&)};
+
+  operator f;
+  let{
+    laplace(df(f(~x),x),x) => il!&*laplace(f(x),x) - sub(x=0,f(x)),
+
+    laplace(df(f(~x),x,~n),x) => il!&**n*laplace(f(x),x) -
+      for i:=n-1 step -1 until 0 sum
+        sub(x=0, df(f(x),x,n-1-i)) * il!&**i
+          when fixp n,
+
+    laplace(f(~x),x) = f(il!&)
+    };
+
+Remarks about some functions:
+
+The DELTA and GAMMA functions are known.
+
+ONE is the name of the unit step function.
+
+INTL is a parametrized integral function
+
+    intl(<expr>,<var>,0,<obj.var>)
+
+   which means "Integral of <expr> wrt <var> taken from 0 to <obj.var>",
+e.g. intl(2*y**2,y,0,x) which is formally a function in x.
+
+We recommend reading the file LAPLACE.TST for a further introduction.