Expression of type Len

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 b, delta, k, theta
from proveit.core_expr_types import Len
from proveit.numbers import Add, Exp, Mult, e, i, pi, two

# build up the expression from sub-expressions
expr = Len(operands = [Exp(e, Mult(Add(Mult(two, pi, i, delta), Mult(two, pi, i, theta)), k)), Exp(e, Mult(two, pi, i, b))])

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

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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