Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, i, n, x
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Interval, Natural, Sum, frac, one, subtract, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(zero, n)), frac(subtract(one, Exp(x, Add(n, one))), subtract(one, x))), And(InSet(x, Complex), InSet(n, Natural), NotEquals(x, one)))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\left(\sum_{i = 0}^{n} x^{i}\right) = \frac{1 - x^{n + 1}}{1 - x} \textrm{ if } x \in \mathbb{C} ,  n \in \mathbb{N} ,  x \neq 1\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10, 11
7	Operation	operator: 12 operand: 20
8	Operation	operator: 14 operands: 15
9	Operation	operator: 34 operands: 16
10	Operation	operator: 34 operands: 17
11	Operation	operator: 18 operands: 19
12	Literal
13	ExprTuple	20
14	Literal
15	ExprTuple	21, 22
16	ExprTuple	47, 23
17	ExprTuple	51, 24
18	Literal
19	ExprTuple	47, 52
20	Lambda	parameter: 39 body: 26
21	Operation	operator: 49 operands: 27
22	Operation	operator: 49 operands: 28
23	Literal
24	Literal
25	ExprTuple	39
26	Conditional	value: 29 condition: 30
27	ExprTuple	52, 31
28	ExprTuple	52, 32
29	Operation	operator: 44 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 37 operand: 41
32	Operation	operator: 37 operand: 47
33	ExprTuple	47, 39
34	Literal
35	ExprTuple	39, 40
36	ExprTuple	41
37	Literal
38	ExprTuple	47
39	Variable
40	Operation	operator: 42 operands: 43
41	Operation	operator: 44 operands: 45
42	Literal
43	ExprTuple	46, 51
44	Literal
45	ExprTuple	47, 48
46	Literal
47	Variable
48	Operation	operator: 49 operands: 50
49	Literal
50	ExprTuple	51, 52
51	Variable
52	Literal

Expression of type Conditional¶

from the theory of proveit.numbers.summation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.summation ¶