docs: cleanup document

crypto3/docs/manual/quickstart.md

@@ -3,7 +3,7 @@
 Quickstart
 ========================
 
-By the end of this guide ,you will have set up a development environment for crypto3 projects 
+By the end of this guide, you will have set up a development environment for crypto3 projects 
 and be able to run an example.This will enable you to test ideas quickly and further explore the 
 API's of the suite.
 

crypto3/libs/algebra/docs/implementation.md

@@ -2,7 +2,7 @@
 
 @tableofcontents
 
-The key idea of `algebra` is to provide usefull interfaces for basic cryptography math. It's based on NilFoundation fork of 
+The key idea of `algebra` is to provide useful interfaces for basic cryptography math. It's based on NilFoundation fork of 
 Boost.Multiprecision so that it can be used with boost cpp_int, gmp or other backends.
 
 We expanded Boost.Multiprecision with `modular_adaptor`, which is actually a multi-precision number by some modular. It contains 

crypto3/libs/blueprint/docs/concepts.md

@@ -1,7 +1,7 @@
 # Concepts # {#component_concepts}
 
 A ```circuit``` is defined by ```Blueprint``` and ```Blueprint assignment table``` (contains ```Blueprint public assignment table``` and ```Blueprint private assignment table```) instances.
-It consist of one or multiple components putted on these two.
+It consists of one or multiple components putted on these two.
 While ```Blueprint``` holds information about the circuit itself, its gates, constraints and other fixed expressions, ```Blueprint assignment table``` contains public and private assignments needed by zk-SNARK system.
 
 ## Blueprint 
@@ -29,4 +29,4 @@ The process of adding a component is following:
 1. (Optional) Get ```component``` start row by calling ```allocate_rows```. If the ```component``` is used as part of other ```component``` logic, it's not necessary to call the function, because needed rows are allocated by the master ```component```.
 2. (Optional) Allocate public input on the ```Blueprint assignment table``` via ```Blueprint assignment table::allocate_public_input```.
 3. Set all the gates and constraints on the ```Blueprint``` by calling ```generate_circuit```. ```Allocated data``` is being modified in process of the function working.
-4. Set all the assignments on the ```Blueprint assignment table``` table by calling ```generate_assignments```.
+4. Set all the assignments on the ```Blueprint assignment table``` table by calling ```generate_assignments```.

crypto3/libs/blueprint/docs/usage.md

@@ -89,7 +89,7 @@ w = [1, 3, 35, 9, 27, 30].
 
 Now let’s see how we can enter this R1CS into =nil;Crypto3 Blueprint, produce proofs and verify them. We will use the `blueprint_variable` type to declare our variables. See the file `test.cpp` for the full code.
 
-First lets define the finite field where all our values live, and initialize the curve parameters:
+First let's define the finite field where all our values live, and initialize the curve parameters:
 
 ```
 typedef libff::Fr<default_r1cs_ppzksnark_pp> field_type;

crypto3/libs/hash/docs/pack.md

@@ -129,7 +129,7 @@ order we have the reverse order of input chunks in the *out* array.
 
 An interested reader may wonder why changing of endiannesses leads to such a strange effect. Well, the answer to this
 question lies in the following convention: all data divided into chunks with units ordered in `big_unit_big_bit`
-endianness will stay unchanged when tranforming to data with chunk units ordered in `big_unit_big_bit` endianness. Let
+endianness will stay unchanged when transforming to data with chunk units ordered in `big_unit_big_bit` endianness. Let
 us explain it with the following example.
 
 ```cpp
@@ -162,7 +162,7 @@ struct1 [label="0x12 | 0x34 | 0x56 | 0x78 | 0x90 | 0xab | 0xcd | 0xef"];
 } @enddot
 
 Here it is easy to see that the data from `input` was just concatenated into the `output` data with no additional
-tranformations. Now, notice that the first and the second example described in this section implicitly rely on the
+transformations. Now, notice that the first and the second example described in this section implicitly rely on the
 above-described convention. In the first example the input data is concatenated in reverse byte order, and in the second
 example the byte order is reversed after the input data concatenation.
 
@@ -214,7 +214,7 @@ To conclude, there are three types of reversals that we must deal with in pack a
 
 In this section we suppose that the chunk type of input and output data is integral.
 
-Data chunk order reversal tranforms a group of consecutive input chunks with units in `InputEndianness` order into an
+Data chunk order reversal transforms a group of consecutive input chunks with units in `InputEndianness` order into an
 output chunk with units in `OutputEndianness` order and can be described as follows.
 
 1. Check whether `InputEndianness` or `OutputEndianness` is `little_bit`. This condition determines the data chunk order