Expression of type ExprTuple

from the theory of proveit.numbers.multiplication

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 ExprTuple, a, b, k, theta
from proveit.numbers import Add, Exp, Mult, e, i, pi, two

# build up the expression from sub-expressions
sub_expr1 = Exp(a, k)
sub_expr2 = Add(a, b)
sub_expr3 = Exp(e, Mult(two, pi, i, b))
expr = ExprTuple(Mult(sub_expr1, Exp(e, Mult(two, pi, i, theta, k)), Exp(sub_expr2, k), sub_expr3), Mult(sub_expr1, Exp(Mult(Exp(e, Mult(two, pi, i, theta)), sub_expr2), k), sub_expr3))

expr:

# 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(a^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k} \cdot \left(a + b\right)^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}, a^{k} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta} \cdot \left(a + b\right)\right)^{k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 32 operands: 3
2	Operation	operator: 32 operands: 4
3	ExprTuple	7, 5, 6, 9
4	ExprTuple	7, 8, 9
5	Operation	operator: 24 operands: 10
6	Operation	operator: 24 operands: 11
7	Operation	operator: 24 operands: 12
8	Operation	operator: 24 operands: 13
9	Operation	operator: 24 operands: 14
10	ExprTuple	28, 15
11	ExprTuple	23, 21
12	ExprTuple	30, 21
13	ExprTuple	16, 21
14	ExprTuple	28, 17
15	Operation	operator: 32 operands: 18
16	Operation	operator: 32 operands: 19
17	Operation	operator: 32 operands: 20
18	ExprTuple	34, 35, 36, 37, 21
19	ExprTuple	22, 23
20	ExprTuple	34, 35, 36, 31
21	Variable
22	Operation	operator: 24 operands: 25
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	Operation	operator: 32 operands: 33
30	Variable
31	Variable
32	Literal
33	ExprTuple	34, 35, 36, 37
34	Literal
35	Literal
36	Literal
37	Variable