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Expression of type Div

from the theory of proveit.physics.quantum.QPE

In [1]:
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 l
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t
In [2]:
# build up the expression from sub-expressions
expr = frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t))))))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
division'inline': uses '/'; 'fraction': numerator over the denominator (also see 'frac' function)fractionfraction('with_inline_style', 'with_fraction_style')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 39
operands: 1
1ExprTuple2, 3
2Operationoperator: 25
operands: 4
3Operationoperator: 25
operands: 5
4ExprTuple7, 6
5ExprTuple7, 8
6Operationoperator: 33
operand: 11
7Literal
8Operationoperator: 33
operand: 12
9ExprTuple11
10ExprTuple12
11Operationoperator: 44
operands: 13
12Operationoperator: 44
operands: 14
13ExprTuple16, 15
14ExprTuple16, 17
15Operationoperator: 30
operands: 18
16Literal
17Operationoperator: 30
operands: 19
18ExprTuple46, 21, 22, 20
19ExprTuple46, 21, 22, 23
20Operationoperator: 25
operands: 24
21Literal
22Literal
23Operationoperator: 25
operands: 26
24ExprTuple27, 28
25Literal
26ExprTuple35, 29
27Operationoperator: 30
operands: 31
28Operationoperator: 33
operand: 42
29Operationoperator: 33
operand: 36
30Literal
31ExprTuple43, 35
32ExprTuple42
33Literal
34ExprTuple36
35Operationoperator: 37
operand: 41
36Operationoperator: 39
operands: 40
37Literal
38ExprTuple41
39Literal
40ExprTuple42, 43
41Literal
42Variable
43Operationoperator: 44
operands: 45
44Literal
45ExprTuple46, 47
46Literal
47Literal